Given that sin CBD= 0.7, calculate (a) the length of BC (b) BEA 4. 9. . 2. Explain how you arrived . 2. B. Expert Answer Transcribed image text: 1 In the diagram below of triangle ABC, AC is extended through point C to point D, and BE is drawn to AC. Geometry (Common Core) Jan. '16 [11] [OVER] Jan. ' 16 [12] Angle BDC = 40 (i) Work out the value of p. (2 marks) (ii) Hence write down the value of q. 5 6 C ADB What is the length of _ . Using the similar triangles you found in part (a), complete the following extended proportion: AB AC 5 DE j 5 j DG 5 j j 1.) In triangle ABC and angle C is the right angle, cos A = 21/5. Which equation can be used to find the value of x? Angle TBA = 62 5 In scalene triangle ABC, m . 3. The lengths of the sides of ABC are 5, 8, and 11. 23. I got 42 degrees! Recall from above that an equilateral triangle is also an isosceles triangle. An equilateral triangle is also called an equiangular triangle since its three angles are equal to 60. What is the perimeter of A . AC such that ^ADB is an equilateral triangle, and ^DBC is an isosceles triangle with DB =BC . In the diagram of ABC below, AB is extended to point D. If mCAB=x+40, mACB=3x+10,mCBD=6x , . 10. . IGCSE Extended: The diagram (not to scale) shows a quadrilateral made up of a number of triangles. WZ=YZ, find ANGLE VYW . BDA 4) In the accompanying diagram, ABC is isosceles, BC extended to D,, AC AB and 80 A m. Find. 6 In the diagram below, ABC is shown with AC extended through point D. If m BCD 6x 2, m BAC 3x 15, and m ABC 2x 1, what is the value of x? Triangle ABD is scalene. He measured CF and found it to be 6 inches. The diagram shows a triangle ABC where AB = AC, BC = AD and Angle BAC = 20 Degrees. Medium. In the diagram below of ^ABC, BC is extended to D. In the diagram of rAEB, !" is extended to R and K, . In ^ABC, OB is congruent to OC. 5 cm 5 cm 15 cm 3 cm 4 cm Find the x-intercept and y-intercept of each linear function In the diagram below of triangle ABC, AC is extended through) point C to point D, and BE is drawn to AC. Question 733053: In the diagram of triangle ABC, side BC is extended to D [IMG]C:\Users\user\Pictures\p16a.gif[/IMG] If m Answer by MathLover1(19462) (Show Source): You can put this solution on YOUR website! BCD 5) An exterior angle at the base of an isosceles triangle measures 110 . BE AC AC. Explain how you know that they are all similar. 7) An isosceles . Find two possible values of CAB 2. 25 Triangle ABC is graphed on axes below. View solution > . 8 In the diagram below of ABC, BC is extended to D . (1 mark) _____ The tangent DB is extended to T. The line AO is added to the diagram. 2x + x = 6 C. 3x + 2x = 6 D. x +2 3 x = 6 page 6 review - triangles 35. 25. The adjoining diagram shows a ray A B. If the length of NLis 6 cm, what is mN? a L S)'nC (2q.B3 = (Total 6 marks) The diagram below shows a triangle and two arcs of circles, The triangle ABC is a right-angled isosceles triangle, with AB midpoint of [BC]. C is 4.5 km due west of turbine B. 21. 10. What is the measure of angle B? O 7.5 O 8.5 AB = 6, AE = 5, and AC = 15 8. If PF = x, which equation can be used to nd x? 6 In isosceles triangle ABC, AB =BC. To ask Unlimited Maths doubts download Doubtnut from - https://goo.gl/9WZjCW In triangle ABC, D and E are two points on the sides AB and AC respectively so t. 16 In the diagram below of triangle ABC, is extended through computations. 6) An exterior angle at the base of an isosceles triangle measures 130 . (1) sin A . STUVWXYZ is a regular octagon. Find the volume of the Triangular Prism below. Look carefully at the diagram below before answering the following questions. Find the perimeter of the triangle formed by connecting the midpoints of the sides of BC. lox - 20 t 30 14) In the diagram below of triangle ABC, AC is extended through point C to point D, and BE is drawn to AC. The interior angles of a convex polygon form an Genius Math Triangle ABC has AC=BC, angle ACB=96 degrees. In ABC, mACB=90, mACD=60, CD is the altitude to AB , and BD = 5 cm. The diagram shows the positions of three turbines A, B and C. Diagram NOT accurately drawn A is 6 km due north of turbine B. A) 10 B) 12.5 C) 20 D) 27.5 6. In diagram below, KLM is a straight line. As shown in the diagram below, CD is a median of triangle ABC. ABC is a triangle where AB=12 cm, AC= 8cmand ABC= 30 . 1) AB 2) DC 3) AD 4) BD 11 In the diagram below of ABC with side AC extended through D, m . b. What is the length of AD to the nearest tenth of a centimeter? What is the measure in degrees of angle ACD? The measure of OB is 20 more than twice the measure of OA. 16. In the diagram of A ABC and A DEF below, AB DE, LA LID, and Z E. Which method can be used to prove . In the accompanying diagram of BCD, ABC is an equilateral triangle and AD = AB.What is the value of x, in degrees? c. (x2 + 5x)0 11 page 2 The arc BDC is part of a circle with . In the diagram below of right triangle ABC , altitude CD is drawn to hypotenuse AB. The section in triangle ADE will be labeled h1 and the section the trapazoid will be h2. GCSE Higher: The angle marked \(x\) in the diagram below is obtuse. 22. Terms and Conditions 2021 Cummins Inc., Direct Marketing, Mail Code 60610, 500 Jackson Street, Columbus, IN 47201 U.S.A. In the diagram below, AB, BC, and AC are tangents to circle O at points F, E, and D, respectively, 6, 5, and BE = 4. 1) 60 2) 120 3) 180 4) 300 2 In the diagram below, RCBT and ABCare shown with mA=60 and mABT=125. Angle ABD = 80 degrees. Find mOABC. Give your answer correct to the nearest degree. 1) mB =mA 2) mA >mB 3) mA =mC 4) mC <mB 7 In the diagram below of ACD, B is a point on AC such that ADB is an equilateral triangle, and DBC is an isosceles triangle with DB BC. In the diagram below of right triangle ABC, AC = 8, and AB = 17. Find the size of angle PQR. . (b) The straight line AB is extended to B' such that BC = B . In the diagram below abc is shown with ac extended In the diagram below, ABCis shown with extended through pointD IfmBCD=6x+2,mBAC=3x+15, and mABC=2x1, what is the value ofx 1) 12 In the diagram below of ABC,BCis extended to D. If mA=x26x,mB=2x3, and mACD=9x+27, what is the value ofxAC. Which equation would determine the value of angle A? 16 44 In the diagram of APQR shown below, PR IS extended to S, m/_P = 110 mZQ = 4x, and m/ QRS x2 + 5x. Find the number of degrees in OB. Name as many pairs . km (3) (b) Calculate the bearing of C from A. Find the value of \(x\) Worked Solution. Which statement about the sides of the triangle is true? Label each one as either perpendicular bisector, altitude, median, or angle bisector. (3 marks) _____ A, B and C are points on the circumference of a circle with centre O. BD and CD are tangents. The diagram shows a triangular prism of length 12 cm. . Prove that triangle QSR is isosceles. Transcribed Image Text: In the diagram of AABC below, AB = 10, BC = 14, and AC= 16. 20 [OVER] If KG (1) 15 (2) 16 9 and IG = 12, the length of 1M is (4) 25 11 Which three-dimensional figure will result when a rectangle 6 inches long and 5 inches wide is continuously rotated about the longer side? In ^ABC, the measure of OB is twice the measure of OA. What is the measure of the vertex angle? On the set of axes below, graph the locus of points 5 units from the point (2;3) and the locus of points 2 units from the line whose equation is y= 1. 24. A. x = 5 B. y = 2 C. y = x D. x + y = 4 7. 18. Use this space for computations. 15 In the diagram below, the length of the legs AC and BC of right triangle ABC are 6 cm and 8 cm, respectively. Also, since DEDF, EF, so by the . Given . Math Geometry Geometry questions and answers 6. a) How many edges does a tetrahedron have? below. (AP)I Geometry Aug. '17 megas C C/ St 5 7/4 E 21 A D Which equation Find m QPT. If mA =66, mCDB =18, and mC =24, what is the longest side of ABD? . The altitude, h, to the hypotenuse has . Solution 1. What is the measure of LA? IB Studies: . D and E are two points on the sides AC and BC respectively of \( \triangle ABC\) such that DE = 18 cm, CE = 5 cm and \(\angle DEC\) = 90. And that that equals 4 times the area of the trapazoid 4 (h2 {DE+20}/2). If mZBCD 300, determine and state mLAOB. a L S)'nC (2q.B3 = (Total 6 marks) The diagram below shows a triangle and two arcs of circles, The triangle ABC is a right-angled isosceles triangle, with AB midpoint of [BC]. Francisco needs the three pieces of glass shown below to complete a stained glass window. See the answer -- 10k ($3 angles that are 65 7-51) 64 CIO t 54 cc -9 13) Find the measure of zj in the diagram below. Consider the triangle ABC where AB=17cm, AC=14cm and the angle BAC = 118 o. below, ED is extended to A, and AF is drawn such . The area of the triangle is 50 cm . The following is a power of a point solution to this menace of a problem: In an isosceles triangle, the base angles are congruent. In triangle PQR, PQ is 12 cm, QR is 10 cm and angle PQR is acute. 5 In the diagram below, ABC is inscribed in circle P. The distances from the center of circle P to each side of the triangle are shown. 1) a reflection over the x-axis followed by a translation 2) a reflection over the y-axis followed by a translation 3) a rotation of 180 about the origin followed by a translation 4) a counterclockwise rotation of 90 about the origin followed by a translation 21 The coordinates of the endpoints of QSare Q(9,8) and S(9,4). Triangle ABC is similar to triangle DEF . In diagram below, ABC and BED are straight lines, E is the mid-point of BD . Find four similar triangles. 1) 125 2) 115 3) 65 4) 55 3 Given ABCwith mB=62 and side AC The sum of the interior angles of a polygon of n sides is A. 2) 15 27 17. Answer(a)(iii) m2 [2] (b) X Y 12 cm 22 cm 45 cm NOT TO SCALE A cuboid has length 45 cm, width 22 . In the diagram below, the length of the legs AC and BC of right triangle ABC are 6cm and 8cm, respectively.Altitude CD is drawm to the hypotenuse of triangle ABC. BC and EF ? The intersection of the angle bisectors of a triangle is the center of the . sides of equilateral triangle ABC, and the perimeter of AABC is 36 cm. . Calculate the angle between the line CE and the base ABED. The length of the line segment joining the midpoints of two sides of equilateral triangle ABC is 5. 1) mZl = mZ3 + mZ2 2) mL5 = mZ3mZ2 1 In the diagram below, _ AB , _ BC , and _ AC are tangents to circle O at . In the diagram of ^PQR shown below, PR is extended to S, mOP = 110, mOQ = 4x, and . ? [Only an algebraic solution will be accepted.] 1) rotation 2) dilation 3 . ection over which line does not carry the square onto itself? Show that the train decelerates for 60 seconds until it . Triangle ABC is a right triangle with the right angle at C. Which are possible measures for angle A and angle B? In the accompanying diagram of . Angle BAC = 90, AC = 6 cm and AB = 5 cm. 2x 1 13 15 B 16 O 7 8. And the area of the small triangle + the area of the trapazoid also equals the area of the large triangle. 21 C D A m2 1 = m2 3+ m22 m26 = m23 - m_2 BmZ5 = m23-m22 Om27 = m_3+ m22 Previous question Next question 31 In the diagram below of AHQP, side HP is extended through P to T, mAQPT = 6x + 20, mAHQP = x + 40, and mAPHQ = 4x - 5. We also now that the area of the large triangle is (h1+h2)20/2. 22. 23 In the diagram below of right triangle ABC, _ CD is the altitude to hypotenuse _ AB , CB = 6, and AD = 5. This diagram shows how a periscope works. Angle A measures 47 degrees and external angle BCD mesures 113 degrees. 360 B. In Figure, sides AB and AC of ABC are extended to points P and Q respectively. Geometry Special Properties and Parts of Triangles Perpendicular Bisectors Since DEEF, the base angles, D and F, are congruent. (2) a reflection over the longer diagonal clockwise rotation of 90 about the intersection of the diagonals ( 4) a counterclockwise rotation of 180 about the intersection of the diagonals 5 In the diagram below of circle 0, points K, A, T, I, and E are on the circle, 6.KAE and 6.ITE are drawn, KE ~ ---EI, ~ and LEKA ---LEIT. Well we will draw the altitude from A. Show Step-by-step Solutions Geometry - June 2012 Regents - Q #26 Equation of a Parallel Line An equation of the line that passes through (2,1) and is parallel to the line 2y + 3x = 8 is A. x + x = 6 B. Find the measure of each angle in ^ABC. As shown in the diagram below, AB and CD intersect at E, and AC k BD. Find the size of angle PQR. Given that the area of triangle ABC is 6 square units, (i) find the coordinates of C. [3] The line CB is extended to the point D so that B is the mid-point of CD. In triangle PQR, PQ is 12 cm, QR is 10 cm and angle PQR is acute. In the diagram of ABC below, AB is extended to point D. 10 IZCAB = X+40, ZACB - 3x + 10, 2CBD=6x, what is CAB? Given right triangle ABC with a right angle at C, m . (3) 1180 1210 Which value of x makes AB (1) 590 (2) 620 12 In the diagram shown below, PA is tangent to circle T at A, and secant P BC is drawn where point B is on circle T. an C = 15 what is the length of PA? If ^RST ^ABC, mOA = x2 8x, mOC = 4x 5, and mOR = 5x + 30, nd mOC. Find mAQPT. 10 In the diagram below of right triangle Kill, altitude IG is drawn to hypotenuse KM. Which equation is always true? In a triangle ABC, the side BC is extended up to D such that CD = AC. Worked Solution. . Which statement is ALWAYS true? In the diagram below, A ABC is circumscribed about circle O and the sides of LABC are tangent to the circle at points D, E, and F. If AB = 20, AE = 12, and CF= 15, what is the length of AC? what is the lenght of AD to the nearest tenth of a centimeter? What is mACR? In the diagram below of triangle ABC, BC is extended to D. If mA = x 2 6x, mB = 2x 3, and mACD = 9x + 27, what is the value of x? 3. Answer (1 of 4): I think you're asking the following. 27 In the diagram below of ABC, side _ BC is extended to point D, m . If the two mirrors are parallel and 1 3, what is m6 when m2 90 ? Altitude CD is drawn to the hypotenuse of ABC. . Unformatted text preview: Unit 7: Similar Figures Project Task 1 In the diagram below, AC 6 DF 6 BH and CB 6 FE.A D C G B H F E a. 17. Use this space for computations. 7. What is Angle ADB? Find AD. In a triangle ABC, AB=AC and D is a point on side AC such that BCxBC=ACxCD. What is the length of the shortest side of DEF if its perimeter is 60? The intersection of the angle bisectors of a triangle is the center of the inscribed circle. In the diagram below, ^ABC is shown with AC extended through point D. \(ABC\) is the equilateral triangle with sides \(AB = BC = AC = a.\) So, the perimeter of \(\Delta ABC = \) the length of the sides \( = AB + BC + CA = a + a + a = 3a = 3 \times {\rm{side}}\) Formula for area of a triangle. Calculate (a) JLK (b) LJM 3. (a) Calculate (i) BAC. 10 7. Draw diagram to show : line A B. recall: Do not use staples, paper clips, glue or correction fluid. 1. 2 In the diagram below, ABC with sides of 13, 15, and 16, . Let be an acute triangle with circumcircle and let be the intersection of the altitudes of Suppose the tangent to the circumcircle of at intersects at points and with and The area of can be written in the form where and are positive integers, and is not divisible by the square of any prime. Find the perimeter of ^ABC. 620 620 and side AC extended to D, as shown Use this space for computations. 0 0 9 50 100 150 Time (s) Speed (m/s) 200 250 300 (a) Find the acceleration, in m/s2, of the train during the first 50 seconds.m/s2 [1] (b) After 180 seconds, the train decelerates at a constant rate of 1944 km/h2. B. 8. The diagram shows an isosceles triangle ABC in which A is the point (3, 3), B is the point (6, 3) and C lies below the x-axis. 1) 12 2) 14 10 11 3) 16 4) 18 1 9 7 In the diagram below of HQP, side HP is extended through P to T, m QPT 6x 20, m HQP x 40, and m PHQ 4x 5. In the accompanying diagram, mOA = 2x 30, mOB = x, and mOC = x+ 10. Graph and label AA 'B 'C', the image of AABC 26 In the diagram below of circle O with diameter BC and radius OA, chord DC is parallel to chord IBA. after a reflection over the l. ex = 1. Question 5 120 seconds Q. If the length of diagonal AC is 12, what is the length of DB? 14. (a) Calculate the distance AC. In the accompanying diagram of ^ABC, the measure of exterior angle BCD is 110 and mOBAC = 50. class 8. In the accompanying diagram, parallel lines AB and CD are intersected by transversal at points G and H, respectively, mAGH = x + 15, and mGHD = 2x. In triangle ABC, side AC is extended through C to point D to create external angle BCD. Triangle ABC is a cross section of the prism. answer choices A B C D Question 6 120 seconds Q. Some diagrams, one with no obtuse angles in ABC, and three others with A or B or C obtuse, seem to strongly sug. 5. F 30 G 45 H 50 J 60 5 Sides BC and AC of ABC are extended . D is a point in ABC such that angle DAB=18 degrees and angleDBA=30 degrees. Question: 6. (ii) the length, in cm, of AD. Find the length of BC. The diagram shows a triangle ABC where AB = AC, BC = AD and Angle BAC = 20 Degrees. 37 In the diagram below, ABST is a 3-4-5 right triangle. If EF = 2x + 8 and AB = 7x - 2, what is the perimeter of trapezoid ABFE? In the accompanying diagram of BCD, ABC is an equilateral triangle and AD = AB.What is the value of x, in degrees? 4 times the area of the trapazoid equals the area of the large triangle. Which equation would determine the value of angle A? Let ABC be any triangle. Problem. If working is needed for any question it must be shown below that question. Storms and Cyclones Struggles for Equality The Triangle and Its Properties. Using a compass and straightedge, construct a new equilateral triangle congruent to ^ABC in the space below. The diagram below shows a tetrahedron, which is a three-dimensional solid formed from four equilateral triangular faces: Each face is bounded by three edges, and three edges meet at a single point called a vertex. The angles of triangle ABC are in the ratio of 8:3:4. . Find SW/ TZ. In the diagram below, ^ABC ^ADE. 1) 3.6 2) 6.0 3) 6.4 4) 4.0 16 In the diagram below, tangent AB and secant ACD are drawn to circle O from an external point A, : Find angle C: 180 - 113 = 67 degrees: Find angle B: 180 - A - C = B Algebra. 1) 36 2) 60 If m , m , and m , what is the value of ? Question 6: Diagram below shows trapezium ABCD. In the diagram of equilateral triangle ABC shown below, E and F are the midpoints of AC and BC, respectively. 8 In the diagram below of GJK, H is a point on GJ, Given triangle ABC, with E on side BC and side AB extended past B to D, does line DE necessarily intersect side AC of the triangle. In the diagram below, ^ABC is equilateral. In the accompanying diagram, A ABC and AABD are isosceles triangles Mith mZCAB . 12) Find the measure of zc and zd in the figure below. In triangle ABC, it is given that angle A is 59 degrees and angle B is 53 degrees The altitude from B to line AC is extended until it intersects the line through A that is parallel to segment BC; they meet at K. Calculate the size of angle AKB. AC BD ZEAC ZEBD . How to prove that BD=BC? [Leave all construction marks.] B 3 5 7/4 A E Which equation is always true? In the diagram below, triangle ABC with sides of 13, 15, and 16, is mappe onto triangle DEF after a clockwise rotation of 90 about point P. If DE = %3D -1, what is the value of x? The area of the triangle is 50 cm . Which measurements are justi ed by this . This problem has been solved! You may use an HB pencil for any diagrams or graphs. A) 6 B) 6 . [2] The diagram below shows an . Find . In the accompanying diagram of ^ABC, side AB is extended to D. If mOACB = x + 30, mOCAB = 2x + 10, and mOCBD = 4x + 30, what is the value of x? In the diagram below of AABC, side BC is extended to point D, mZA = What is mZB? In the diagram of AABC below, AB The measure of Z B is 400. 3h 3 . answer choices 2x+x+15=180 Question 8 60 seconds Q. 10 As shown in the diagram of ACD below, B is a point on AC and DB is drawn. If AD =3 and DB =12, what is the length of altitude CD? AC. We set those equal to eachother and we simplify we get DEsquared - 60DE - 1200 = 0 when we use the quadratic formula we get DE=30+10square root 21 Please tell if this is right Thank you D Denis Senior Member