Download Congruent Triangles Review Sheet

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Geometry Regents & Honors
Congruent Triangles
Review Sheet
Part 1: Multiple Choice Practice – Answer the following questions below based on your knowledge
of congruent triangles.
1. In the accompanying diagram of triangles BAT and FLU, ∠" ≅ ∠$ and %" ≅ &$.
Which statement is needed to prove ∆%") ≅ ∆&$* by ASA?
(1)∠% ≅ ∠&
(2)") ≅ $*
(3)∠" ≅ ∠*
(4)%" ∥ &$
2. In the diagram of ∆"%+ and ∆,-& below, "% ≅ ,-, ∠" ≅ ∠,,and +" ≅ &,.
Which method can be used to prove ∆"%+ ≅ ∆,-&?
(1)SSS
(2)SAS
(3)ASA
(4)HL
3. In the accompanying diagram, 01 bisects 2$ and ∠0 ≅ ∠1.
What is the most direct method of proof that could be used to prove ∆023 ≅ ∆1$3?
(1)HL
(2)SAS
(3)AAS
(4)ASA
4. In the accompanying diagram, "% and +, intersect at E, E is the midpoint of "%, and ∠" ≅
∠%.
Which statement can be used to prove ∆",- ≅ ∆%+-?
(1)ASA ≅ ASA
(2)HL ≅ HL
(3)SSS ≅ SSS
(4)SAS ≅ SAS
5. Which statement is not valid for proving that two triangles are congruent?
(1)AAS ≅ AAS
(2)HL ≅ HL
(3)SSA ≅ SSA
(4)SAS ≅ SAS
6. In the accompanying diagram of isosceles triangle ABC, ∠"+% is the vertex angle, +? ⊥ "%,
and M is the midpoint of "%.
Which statement can not be used to justify ∆"+? ≅ ∆%+??
(1)HL ≅ HL
(2)AAS ≅ AAS
(3)SSS ≅ SSS
(4)AAA ≅ AAA
7. In the diagram below, "+-, %+,, "%, and ,-, ∠" ≅ ∠-, and C is the midpoint of "-.
Which theorem justifies ∆"%+ ≅ ∆-,+?
(1)SSS ≅ SSS
(2)SAS ≅ SAS
(3)ASA ≅ ASA
(4)SSA ≅ SSA
8. When writing a geometric proof, which angle relationship could be used alone to justify that
two angles are congruent?
(1) supplementary angles
(2) vertical angles
(3) adjacent angles
(4) linear pairs of angles
Part 2: Free Response Practice – Answer the following questions below based on your knowledge
of geometry.
9. Given: ", bisects %+ at E.
"% ⊥ %+
,+ ⊥ %+
Prove: ∆"%- ≅ ∆,+-
10. Given: ∆"%+ and ∆-,+, C is the midpoint of %, and "-.
Prove: ∆"%+ ≅ ∆-,+
11. As shown in the figure below, vertical angles have degree measures of A and 2A − 35. Find
the value of A.
12. In the diagram below, ∆"%+ and ∆DEF are graphed.
Use the properties of rigid motions to explain why ∆"%+ ≅ ∆DEF.
Summary: