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4. In AMTK, MT = TK, mZM = 5x -10 and mZK = 3x + 20. 5. In AMER, ME= ER, mZM = 7x -4 and mZR = 5x + 12.

4. In AMTK, MT = TK, mZM = 5x -10 and mZK = 3x + 20. 5. In AMER, ME= ER, mZM = 7x -4 and mZR = 5x + 12.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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4. In AMTK, MT = TK, mZM = 5x -10 and mZK = 3x + 20. 5. In AMER, ME= ER, m²M = 7x -4 and mZR = 5x + 12.
Transcribed Image Text:4. In AMTK, MT = TK, mZM = 5x -10 and mZK = 3x + 20. 5. In AMER, ME= ER, m²M = 7x -4 and mZR = 5x + 12.
7. ARAE s equinaterar De muoIToI EquIRterau TTRangle Corollary An equiangular triangle is also equilateral. Illustrative Example 2 In isosceles A CAR with base CR, mzC=2x and mZR- x + 35, find the measures of the base angles. R Solution: m2C= mZR Based on the Isosceles Triangle Theorem 2x - x + 35 2х -х - 35 mZR= x + 35 x = 35 m2C = 2(35) m2C - 70° mZR - 35 + 35 mZR - 70° Answer: The base angles are ZC and zR whose measures are 70°each. Illustrative Example 3 Find the length of each side of AZAV given 2Z ZV. 3x - 2 x + 10 x + 4 Solution: Because 2Z ZV, then by The Converse of the Isosceles Triangle Theorem, AZ AV. Based on the definition of congruent segments, AZ - AV. AZ - AV 3x - 2 = x + 10 Зх - х - 1о+2 2x = 12 x - 6 Now replace x with 6 in the expression that represents the measure of each side. AZ - 3x - 2 = 3(6)-2 - 18 -2 - 16 AV - x + 10 Vz - x + 4 -6+ 4 - 10 = 6+ 10 - 16 B. For Right Triangle 1. Consider two right triangles: ANHS and AFOX with right angles at H and O respectively, such that NH = FO and HS = Ox. N F
Transcribed Image Text:7. ARAE s equinaterar De muoIToI EquIRterau TTRangle Corollary An equiangular triangle is also equilateral. Illustrative Example 2 In isosceles A CAR with base CR, mzC=2x and mZR- x + 35, find the measures of the base angles. R Solution: m2C= mZR Based on the Isosceles Triangle Theorem 2x - x + 35 2х -х - 35 mZR= x + 35 x = 35 m2C = 2(35) m2C - 70° mZR - 35 + 35 mZR - 70° Answer: The base angles are ZC and zR whose measures are 70°each. Illustrative Example 3 Find the length of each side of AZAV given 2Z ZV. 3x - 2 x + 10 x + 4 Solution: Because 2Z ZV, then by The Converse of the Isosceles Triangle Theorem, AZ AV. Based on the definition of congruent segments, AZ - AV. AZ - AV 3x - 2 = x + 10 Зх - х - 1о+2 2x = 12 x - 6 Now replace x with 6 in the expression that represents the measure of each side. AZ - 3x - 2 = 3(6)-2 - 18 -2 - 16 AV - x + 10 Vz - x + 4 -6+ 4 - 10 = 6+ 10 - 16 B. For Right Triangle 1. Consider two right triangles: ANHS and AFOX with right angles at H and O respectively, such that NH = FO and HS = Ox. N F
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