NAME _____________________________________________ DATE ____________________________ PERIOD _____________
4-4 Guided Notes
Congruent Triangles
Congruence and Corresponding Parts
Triangles that have the same size and same shape are congruent triangles.
Two triangles are congruent if and only if all three pairs of corresponding
angles are congruent and all three pairs of corresponding sides are congruent.
In the figure, △ABC ≅ △RST.
Third Angles
Theorem
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles
of the triangles are congruent.
Example: If △XYZ ≅△RST, name the pairs of congruent angles and congruent sides.
Example: If △ADE ≅△CBE, name the pairs of congruent angles and congruent sides.
Proving Triangles Congruent—SSS, SAS
SSS Postulate You know that two triangles are congruent if corresponding sides are congruent and corresponding angles
are congruent. The Side-Side-Side (SSS) Postulate lets you show that two triangles are congruent if you know only that
the sides of one triangle are congruent to the sides of the second triangle.
SSS Postulate
If three sides of one triangle are congruent to three sides of a second triangle, then the triangles
are congruent.
Example: Write a two-column proof.
Write a two-column proof.
Given:̅̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝑋𝑌, ̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅
𝑋𝑍 , ̅̅̅̅
𝐵𝐶 ≅ ̅̅̅̅
𝑌𝑍
Prove: △ABC ≅ △XYZ
1.
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Glencoe Geometry
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
4-4 Guided Notes (continued)
Proving Triangles Congruent—SSS, SAS
Example: Write a two-column proof.
Write a two-column proof.
2.
̅̅̅̅ ≅ 𝑈𝑇
̅̅̅̅
̅̅̅̅, 𝑅𝑇
̅̅̅̅ ≅ 𝑈𝑆
Given: 𝑅𝑆
Prove: △RST ≅ △UTS
SAS Postulate Another way to show that two triangles are congruent is to use the Side-Angle-Side (SAS) Postulate.
SAS Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included
angle of another triangle, then the triangles are congruent.
Exercises
Write the specified type of proof.
1. Write a two column proof.
̅̅̅̅̅⊥ 𝑃𝐿
̅̅̅̅
Given: NP = PM, 𝑁𝑃
Prove: △NPL ≅ △MPL
2. Write a two-column proof.
̅̅̅̅ ∥ 𝐶𝐷
̅̅̅̅
Given: AB = CD, 𝐴𝐵
Prove: △ACD ≅ △CAB
3. Write a paragraph proof.
Given: V is the midpoint of ̅̅̅̅
𝑌𝑍
̅̅̅̅̅
V is the midpoint of 𝑊𝑋
Prove: △XVZ ≅ △WVY
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Glencoe Geometry