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Geometry 300
4.4 and 4.5 Tests for Congruent Triangles
Name __________________________
Date ____________________
Warm Up: #1 ∆RST and ∆XYZ represent the triangles. If ∆RST≅ ∆XYZ, identify all pairs of congruent
parts.
Warm Up #2: Given ∆𝐸𝐹𝐻 ≅ ∆𝐺𝐹𝐻, find x and find 𝑚∠𝐺𝐹𝐻.
Objective: By the end of the lesson you will be able to:


Use SAS, SSS, AAS, HL and ASA postulates to test for triangle congruence.
Utilize triangle congruence theorems to prove two triangles congruent
SSS Postulate( Side-Side-Side): If three sides of one triangle are congruent to three
sides of another triangle, then the triangles are congruent.
Example 1: Use SSS to explain why ⊿𝑃𝑄𝑅 ≅ ∆𝑃𝑆𝑅
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅ and 𝐴𝐷
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅
Example 2: Mark the congruent corresponding parts given 𝐴𝐵
Geometry 300
4.4 and 4.5 Tests for Congruent Triangles
Name __________________________
Date ____________________
SAS Postulate (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two
sides and an included angle of another triangle, then the two triangles are congruent.
Example 3: Use SAS to explain why ∆𝑉𝑍𝑊 ≅ ∆𝑋𝑍𝑌.
Example 4: Mark the congruent corresponding parts given ̅̅̅̅
𝐴𝐷 ∥ ̅̅̅̅
𝐺𝑅 and ̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐺𝑅
ASA Postulate (Angle-Side-Angle): If two angles and the included side of one
triangle is congruent to two angles and the included side of another triangle,
then the triangles are congruent.
Example 5: Use ASA to explain why ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐸 if ∠𝐴 and ∠𝐷 are right angles,
and ̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅
𝐷𝐶
̅̅̅ and ̅𝑆𝑇
̅̅̅ bisects ∠𝑅𝑆𝐿.
Example 6: Mark the congruent corresponding parts given ̅̅̅̅
𝑅𝐿 ⊥ ̅𝑆𝑇
Geometry 300
4.4 and 4.5 Tests for Congruent Triangles
Name __________________________
Date ____________________
AAS Postulate (Angle-Angle-Side ): If two angles and a non-included side of one triangle are congruent
to the corresponding two angles and side of a second triangle, the two triangles are congruent.
̅̅̅̅ ∥ 𝑅𝑆
̅̅̅̅ and ∠𝑄 = ∠𝑆 = 90, explain why ⊿𝑃𝑅𝑆 ≅ ⊿𝑃𝑅𝑄.
Example 7: PQRS is a rectangle where 𝑃𝑄
Example 6: Mark the congruent corresponding parts given ̅̅̅̅
𝐴𝐵 ⊥ ̅̅̅̅
𝐵𝐶 , ̅̅̅̅
𝐷𝐸 ⊥ ̅̅̅̅
𝐸𝐹 , ̅̅̅̅
𝐵𝐶 ∥ ̅̅̅̅
𝐹𝐸 and ̅̅̅̅
𝐴𝐹 ∥ ̅̅̅̅
𝐶𝐷
HL (Hypotenuse –Leg) Postulate : If the hypotenuse and leg of one right triangle are congruent
to the corresponding parts of another right triangle, the right triangles are congruent.
Example 7: State the leg that would make ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷 by 𝐻𝐿 ≅ 𝐻𝐿.
Example 8: True or False? The two legs of a right triangle measure 5 and 12. The leg and
hypotenuse of another right triangle measure 12 and 13 respectively. These two triangles are
congruent.
Geometry 300
4.4 and 4.5 Tests for Congruent Triangles
Name __________________________
Date ____________________
Practice Problems:
Which postulate can be used to prove the triangles congruent? If it is not possible to prove them
congruent, then say so.
1.
2.
3.
4.
Mark all congruent parts in each figure, complete the congruency statement, and identify the
postulate that proves the triangles congruent.
5.
6.
Given: HK bisects GKN
Given: BCA  DCE
G   N
B and D are right triangles
BC  CD
Prove: GKH   _________
Prove: CAB   _________
Reason:__________________
Reason:____________________