Title Theory practice.pdf ✅

110 Geometriy 7 A. The Concept of Congruence 1. Find two pairs of congruent figures in each picture. Draw each pair. a. b. EXERCISES 3.2 2. In the figure, polygon ABCDE is congruent to polygon KLMNP. Find each value, using the information given. a. x b. y c. n d. a e. b + 3 : 9; 9* 93 3 :9; 6 *6 4. A triangle ABC is congruent to a second triangle KMN. Find the unknown value in each statement, using the properties of congruence. a. AC = 5m – 25, KN = 11 – m b. m(BCA) = 45° – v, m(MNK) = 2v – 15°, c. m(B) = 18°, m(M) = u – 4°, d. BA = 22x – 30, MK = 3 – 2x 5. Two triangles ABC and CMN are congruent to each other with AB = 8 cm, CN = 3 cm, and CM = AC = 6 cm. Find BC and MN. B. Constructions 6. Construct each angle. a. 15° b. 105° c. 75° d. 37.5° e. 97.5° 3. ADE  KLN is given. List the congruent corresponding segments and angles of these triangles. 7. a. Construct an isosceles triangle with base 5 cm and perimeter 19 cm. b. Construct an equilateral triangle with perimeter 18 cm. c. Try to construct a triangle with sides of length 2 cm, 3 cm and 6 cm. What do you notice? Can you explain why this is so? d. Construct a triangle ABC with side lengths a = 5 cm and c = 7 cm, and m(B) = 165°. e. Construct a right triangle ABC in which m(C) = 90°, b = 5 cm and the hypotenuse measures 7 cm. f. Construct ABC with angles m(C) = 120° and m(B) = 45°, and side b = 5 cm. g. Construct an isosceles triangle PQR with vertex angle m(Q) = 40° and side QP = 3 cm. In each case, construct a triangle using only the three elements given. a. a, b, Vc b. a, b, hc c. a, b, nC d. ha, hb, hc e. A, a, ha f. Va, Vb, Vc 8. 
Triangles and Construction 111 12. In a triangle KLM, m(LKM) = 30°, m(LMK) = 70° and m(KLM) = 80°. O  int KLM and KO = LO = MO are given. Find m(OKM), m(OML) and m(OLK). 10. In the figure, AB = BC, AD = DB and BE = EC. If DC = 3x + 1 and AE = 4x – 1, find the length x. 11. In a triangle DEF, m(E) = 65° and m(F) = 15°, and DK is an angle bisector. Prove that DEK is isosceles. C. Isosceles, Equilateral and Right Triangles 9. KMN is an isosceles triangle with base KN. The perpendicular bisector of the side MK intersects the sides MK and MN at the points T and F, respectively. Find the length of side KN if P(KFN) = 36 cm and KM = 26 cm. 13. In the figure, ABC is an equilateral triangle. PE  BC, PD  AC, PE = 3 and PD = 5 are given. Find the length of one side of the equilateral triangle. 5 14. In the figure, ABC is an equilateral triangle, PE  AC, PD BC, and PF AB. Given P(ABC) = 45, find the value of PD + PE + PF. 15. In the figure, BH = HC, AB = DC and m(B) = 54°. Find m(BAC). 5 7 16. In the figure, BE = EC and AD bisects the interior angle A. Given AB = 12 and AC = 7, find the length of ED. * 3 17. In the figure, O is the center of the inscribed circle of ABC, OB = CD, AB = AC and m(ECD) = 20°. Find the measure of BEC. - * 7 18. In a right triangle ETF, the perpendicular bisector of the leg ET intersects the hypotenuse at the point M. Find m(MTF) if m(E) = 52°. 19. In triangle DEF, DE = EF, m(DEF) = 90° and the distance from E to DF is 4.8 cm. Find DF.
112 Geometriy 7 29. In the figure, m(BAC) = 90°, m(AHC) = 90°, m(B) = 30° and HC = 1 cm. Find the length of BH. 7 30. In the figure, m(DBA) = 30°, m(ABC) = 60° and AD = 4. Find the length of BC. 7 26. In a triangle ABC, BC = 7ñ2, m(BAC) = 30° and m(BCA) = 45°. Find the length of the side AB. 27. The larger acute angle A in an obtuse triangle ABC measures 45°. The altitude drawn from the obtuse angle B divides the opposite side into two segments of length 9 and 12. Find the length of the side BC. 28. In the figure, m(M) = 150°, LM = 2 and MN = 3ñ3. Find the length of KL. + * 7 5 22. In the figure, BC = 12, m(BAC) = 90°, m(ADC) = 90° and m(ABC) = 60°. If AC is the angle bisector of C, find the length of AD. * 7 24. In the figure, m(A) = m(B) = 60°, AD = 7 and BC = 4. Find DC. 3 7 25. In the figure, AB = AC, AD = DB and CD = 8 cm. Find the length of DB. 7 23. In the figure, m(A) = 30° and AB = AC = 16 cm. Find the value of PH + PD. In the figure, PMN is a right triangle, MH  PN and m(N) = 15°. Find (Hint: Draw the median to the hypotenuse.) MH PN . 21.  5 20. TF is the hypotenuse of a right triangle TMF, and the perpendicular bisector of the hypotenuse intersects the leg MF at the point K. Find m(KTF) given m(MTF) = 70°.
Triangles and Construction 113 34. In the figure, m(A) = 90°, m(ADC) = 60°, m(B) = 30° and BD = 4 cm. Find the length of AD. 7 31. ABC in the figure is an equilateral triangle. BH = 5 cm and HC = 3 cm are given. Find the length AD = x. 33. In the figure, ABC is an equilateral triangle, BD = 4 cm and AE = 6 cm. Find the length of EC. 7 32. In the figure, m(C) = 90°, m(BAD) = m(DAC), BD = DA and DC = 3 cm. Find the length of BD. 7 5 38. In the figure, NK is the bisector of the interior angle N and NL = LK. m(NMP) = 90° and m(P) = 24° are given. Find m(PSM). * + 7 39. In the figure, m(BAE) = m(DAE) = 60°, CB = 6 cm and CE = 3 cm. Find the length of CD. 35. In the figure, ABC is an equilateral triangle, PE  AC and PD  AB. PD = 5 cm, PE = 3 cm and P(ABC) = 48 cm are given. Find the length of PH. 5 7 37. In the figure, ABC is an isosceles triangle, AB = AC, m(BAC) = 30° and 2PE = PD = 4. Find AC. * 36. In a right triangle KLM, m(KLM) = 90° and the perpendicular bisector of the leg LM cuts the hypotenuse at the point T. If m(LMK) = 20°, find m(TLK). 40. In the figure, AB = BC m(ADB) = 30° and AC = 6. Find the length of CD. 7