Download Section 4.2 ~ Congruence and Triangles

Section 4.2 ~ Congruence and Triangles
Topics in this lesson:
• congruent figures
• corresponding parts
• Third Angles Theorem
Vocabulary
congruent figures ­ all the parts of one figure are congruent to the corresponding parts of the other figure
corresponding parts ­ the corresponding sides and corresponding angles in congruent polygons
Example 1
Identify all pairs of congruent corresponding parts. Then write a congruence statement for the triangles.
Corresponding angles: Corresponding sides:
Congruence statement:
Very important!!!
When stating that Δs are ≅, the corresponding vertices must be written in a corresponding order.
Example 2
In the diagram, QRST ≅ WXYZ.
a. Find the value of x.
b. Find the value of y.
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.
If A ≅ D and B ≅ E, then C ≅ F.
Example 3 ­ Prove that the triangles are congruent.
When proving triangles ≅, you must have all the ≅ parts listed as steps somewhere in the proof.
Statements
1.
Reasons
1. Given
.
Example 4 ­ Prove that the triangles are congruent.
Given: E is the midpoint of AC and BD.
AB ≅ CD
AB CD
Prove: ABE ≅ CDE Statements
1.
Reasons
1. Given .