Chapter 4- Triangle Congruence

_{4.1 }Classify the triangle by its angle measure. obtuse triangle right triangle equlangular triangle acute triangle _{4.1 }Classify the triangle by its angle measure. obtuse triangle right triangle equlangular triangle acute triangle 86 ^{o}64 ^{o}_{4.1 }Classify the triangle by its side length. isosceles triangle scalene triangle equilateral triangle right triangle _{4.1 }Classify the triangle by its side length. equilateral triangle right triangle scalene triangle isosceles triangle Find the measure of ∡A 4.2 m∡A = B o 25 ^{o}C 127 ^{o}x A 4.1 Find the measure of ∡A m∡A = B 25 ^{o}o x A C 4.1 Find the measure of ∡A m∡A = A o x ^{51o}B C 4.1 Given ∆ABC, find the value of x and the length of side AC x = AC = A 2x + 7 4x - 3 B 3x - 5 C 4.2 Given the following diagram of ∆CDB. Find the value of x x = A x ^{o}o B 52 ^{o}C D Given the following diagram of ∆CDB. Find the value of x 4.2 x = C x ^{o}o 60 ^{o}D B ^{112o}A 4.2 Given the following diagram of ∆CDB. Find the value of x x = A x ^{o}o B 52 ^{o}C D Given the following diagram of ∆CDB. Find the value of x.Then find the measureof the exterior angle. 4.2 ^{(2x + 16)o}A x = C m∡ACD = ^{58o}D B (x + 12) ^{o}o 4.3 Given that ∆FUN ≅ ∆TEA, identify the congruent corresponding parts. ∡N ≅ ∡ AT ≅ use capital letters for answers 4.3 Given that polygon MATH ≅ LOVE identify the congruent corresponding parts. ∡V ≅ ∡ AT ≅ use capital letters for answers 4.3 Given that ∆THE ≅ ∆SUP, and that UP = 2x + 12, and HE = 4x - 50. Find the value of x Find the length of UP UP = x = ^{4.3}Given that polygon PINK ≅ polygon BLUE, how many pair of congruent parts are there? 6: 3 pairs of angles & 3 pairs of sides 4: 4 pairs of angles only 3: 3 pairs of sides only 8: 4 pairs of sides & 4 pairs of angles Given that ∆TEA ≅ ∆CUP, find the value of x and y. 4.3 T 3x - 7 x = 52 ^{o}E A U P y = 11.9 y C Given that ∆HOP ≅ ∆RUF, and themeasure of ∡H = 32 ^{o} and the measure of ∡O = 77^{o. }^{}Find the measure of the following: m∡P = m∡R = m∡U = o o o 4.4 Tell if and why the triangles are congruent. Not congruent, not enough info ∡A ≅ ∡C, thus ∆'s are ≅ by SAS ∆≅ Thm. BD ≅ BD, thus ∆'s are ≅, by SSS ∆≅ Thm. ∆'s are ≅ by the definition of ≅∆'s A B D C 4.4 Tell if and why the triangles are congruent. Not congruent, not enough info AB ≅ AC, thus ∆'s are ≅ by SSS ∆≅ Thm. BD ≅ BD, thus ∆'s are ≅, by SAS ∆≅ Thm. ∆'s are ≅ by the definition of ≅∆'s A B D C ^{4.4}Tell what value x must be in order for the two triangles to be congruent by SSS ∆≅ Thm. 6x - 4 B x = A C 4x + 7 D ^{4.4}Tell if and how the two triangles are congruent. C A Not congruent, not enough info AC ≅ED, thus ∆'s are ≅ by SSS ∆≅ ∡ABC ≅EBD, thus ∆'s are ≅ by SAS ∆≅ B D E ^{4.5}Identify the postulate or theorem that proves the two triangles are congruent. not congruent, not enough info ∡B≅∡D, thus ∆'s ≅ by AAA ∆≅ thm. AC ≅ AC, thus ∆'s≅ by ASA ∆ ≅ thm. AB ≅CD, thus ∆'s ≅ by AAS ∆ ≅ thm. A B D C ^{4.5}What additional information do you need to know in order to prove ∆ABC ≅ ∆EBD by ASA? ∡BDE ≅ ∡BCA ∡A ≅ ∡C AC ≅ ED ∡B ≅ ∡B A D B E C ^{4.5}Identify the postulate or theorem that proves the two triangles are congruent. A not congruent, not enough info ∆'s ≅ by AAA ∆≅ thm. ∆'s≅ by ASA ∆ ≅ thm. ∆'s ≅ by AAS ∆ ≅ thm. ▼ B E ▼ D C ^{4.5}Identify the postulate or theorem that proves the two triangles are congruent. not congruent, not enough info ∆'s ≅ by HL ∆≅ thm. AC ≅ AC, thus ∆'s≅ by ASA ∆ ≅ thm. ∆'s ≅ by SAS ∆ ≅ thm. A D B C ^{4.5}Identify the postulate or theorem that proves the two triangles are congruent. A not congruent, not enough info ∆'s ≅ by AAA ∆≅ thm. ∆'s≅ by SAS ∆ ≅ thm. ∆'s ≅ by ASA ∆ ≅ thm. ▼ B E ▼ D C ^{4.6} False True; ∆'s ≅ by SAS, and AT ≅ UC by CPCTC True; ∆'s ≅ by ASA, and AT ≅ UC by def. ≅ sides True; ∆'s ≅ by SAS, and AT ≅ UC by SSS Tell if the highlighted statementis true or false and why (if it's true). AT ≅ UC T A E P U C ^{4.6} True; ∆'s ≅ by SAS, and ∡T ≅ ∡C by CPCTC True; ∆'s ≅ by SSS, and AT ≅ UC by SAS False True; ∆'s ≅ by SAS, and ∡T ≅ ∡C by Third ∡ Thm. Tell if the highlighted statementis true or false and why (if it's true). ∡T ≅ ∡C T A E P U C Tell if (and why) the highlighted statement is true. ∆'s ≅ by SSS, Thus true by CPCTC ∆'s ≅ by SSS, Thus false ∡'s ≇ ∆'s ≅ by SAS , Thus true by CPCTC ∆'s are not ≅, thus false ∡'s ≇ ∡A ≅ ∡B A C B D 4.6 Match the theorem that proves the ∆'s are ≅ A. SSS B. SAS C. AAS D. ASA E. HL ∆'s ≅ Choose from: use capital letters ∆'s ≅ ∆'s ≅ ^{4.8}A C Find the measure ∡A & ∡B m∡A= D 24 ^{o}m∡B= 76 ^{o}B E ^{4.8}Find the measure ∡A & ∡DBC m∡A= m∡DBC= A D 45 ^{o}C B ^{4.8}Find the measure ∡A & the value of x m∡A= x = B C A (7x - 3) ^{o}^{4.8}Find the measure ∡A, the value of x, and the length of AB m∡A= x = AB = (3x + 3) B C (5x - 17) A Find the measure ∡B, the value of x, and the length of CA ^{4.8}m∡B= CA = x = (½x + 6) B (2x) C (2x) A ^{4alg}Solve for x. 5 2 x + 7 = 22 x = ^{4alg}Solve for x. 3 4 x - 4 = 14 x = ^{4alg}Solve for x. 5 4 x + 7 = x = 3 2 x + 3 ^{4alg}Solve for x. 3x ^{2} = x^{2} + 50x = ^{4alg}Solve for x. -2x ^{2} = -3x^{2} + 144x = Find the missing angle measures for ∡1 & ∡2 m∡1 = m∡2 = 37 ^{o}o o 1 77 ^{o}2 |

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