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Download ASSIGNMENT: CPCTC, Equilateral and Isosceles Triangles
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NAME:___________________________________! DATE: 10/21/2013 ASSIGNMENT: CPCTC, Equilateral and Isosceles Triangles DIRECTIONS: Congruent parts in congruent triangles are congruent. In other words, make sure you look at the congruency statements to identify corresponding congruent angles and sides. Equilateral triangles are equiangular; isosceles have two congruent sides with congruent base angles. 1.) Find the value of b ! ! ! ! 4a! ! ! ! ! ! ! ! (10a + b)º!! ! ! ! ! ! ! 2.) ! ! ! ! T! ! ! ! ! X!! ! ! ! 41º! ! ! ! Y ! V! ! ! ! ! ! ! ! ! 40º! ! a + 9! 2! ! ! ! ! ! ! ! ! ! ! ! A: b = 3/2 B: b = 15 C: b = 25 D: b = 40 E: b = 10 Find the measure of ∠XVY. ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! U! ! ! ! ! A: m∠XVY = 41º B: m∠XVY = 82º C: m∠XVY = 98º D: m∠XVY = 180º E: m∠XVY = 102º 3.) Determine if each statement is sometimes (S), always (A), or never (N) true. 3a.) An equilateral triangle is an isosceles triangle. ______ 3b.) An isosceles triangle is an equiangular triangle. ______ 3c.) An equiangular triangle and an acute triangle are congruent. ______ 3d.) One of the base angles in an isosceles triangle is obtuse. ______ 3e.) The vertex angle of an isosceles triangle is congruent to the base angles. ___ 4.) Rachel is designing a logo for an app she created for the new iPhone. The app provides an automatic filter of YouTube videos that show educational parodies of secular music. She wants to design the logo such that the four corners of the rectangular logo are all 90 degrees. She also wants the diagonal lines to be congruent. If the two diagonal lines meet at a 20º angle, what is the measure of the angles opposite the angles?!! ! ! ! ! ! ! ! ! ! ! ! ! ! what is this angle? ! ! ! ! A: 20º! D: 50º! ! ! ! ! ! ! ! ! B: 60º! C: 5º E: 80º! F: 10º ! ! ! ! Rachel’s MATH RAP Finder 20º ! ! what is this angle? NAME:___________________________________! 5.) ! ! ! ! ! ! ! ! ! ! ! ! ! rº!! ! ! ! ! 121º! ! ! ! DATE: 10/21/2013 ! ! Find the measure of ∠r. ! ! 146º! ! ! ! ! ! ! ! ! ! ! ! ! A: m∠r = 87º B: m∠r = 59º C: m∠r = 34º D: m∠r = 121º E: m∠r = 46º 6.) In ∆ABC, AB = 2d + 10, BC = 5d − 2, and AC = d + 16. If ∆ABC is equiangular, what is the value of d?! ! ! 2 A: d = 1 ! B: d = 2! C: d = 3! D: d = 4! E: d = 5! F: d = 6 7.) In the figure below, ∠GFH and ∠GHF are congruent. Which of the following ! ! ! G!! ! ! ! statements are true? ! ! ! ! ! ! ! ! ! ! ! ! ! a) m∠GHJ > m∠HGF ! ! ! ! ! ! ! b) m∠GFH = m∠GHF ! ! ! ! ! ! ! c) m∠FGH + m∠GFH > m∠GHJ F ! ! ! ! ! ! ! H! ! J A: a only! ! B: b only! D: b and c only! ! ! ! ! D! A!! ! ! ! C: a and b only! ! E: a, b, and c 8.)! ! ! ! ! 2c − 6! F ! E ! ! ! ! 9c − 34! 10c ! ! ! ! ! ! ! 9.) ! ! For what value of “c” is A: c = 1 ! B: c = 2! E: c = 5! F: c = 6 DEF isosceles? C: c = 3! D: c = 4 ! C ! ! 62º! ! B! ! ! (2a−5)º If ∠ACB ≅ ∠BCD, what is the value of “a”? D! ! A: a = 32.75! ! B: a = 62! ! C: a = 59 D: a = 108! ! E: a = 5! ! F: a = 60.5
