1. Congruence and Triangles
4-2
Congruence and Triangles
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz

2. 4.2 Congruence and Triangles
Warm Up
1. Find the measure of exterior DBA of BCD, if mDBC = 30°, mC= 70°, and mD = 80°.
2. What is the complement of an angle with measure 17°?
3. How many lines can be drawn through N parallel to MP? Why?
150°
73°
1; Parallel Post.

3. 4.2 Congruence and Triangles
When two figures are congruent, there is a correspondence between their angles and sides such that corresponding angles are congruent and corresponding sides are congruent.

4. 4.2 Congruence and Triangles

5. Example 1: Proving Two Triangles are Congruent
4.2 Congruence and Triangles
Example 1: Proving Two Triangles are Congruent

6. Example 1: Proving Two Triangles are Congruent
4.2 Congruence and Triangles
Example 1: Proving Two Triangles are Congruent

7. 4.2 Congruence and Triangles

8. Example 2: Applying the Third Angles Theorem
4.2 Congruence and Triangles
Example 2: Applying the Third Angles Theorem
Find mK and mJ.
K  J
Third s Thm.
mK = mJ
Def. of  s.
4y2 = 6y2 – 40
Substitute 4y2 for mK and 6y2 – 40 for mJ.
–2y2 = –40
Subtract 6y2 from both sides.
y2 = 20
Divide both sides by -2.
So mK = 4y2 = 4(20) = 80°.
Since mJ = mK, mJ = 80°.

9. 4.2 Congruence and Triangles
Check It Out! Example 2
Find mP and mT.
P  T
Third s Thm.
mP = mT
Def. of  s.
2x2 = 4x2 – 32
Substitute 2x2 for mP and 4x2 – 32 for mT.
–2x2 = –32
Subtract 4x2 from both sides.
x2 = 16
Divide both sides by -2.
So mP = 2x2 = 2(16) = 32°.
Since mP = mT, mT = 32°.

10. 4.2 Congruence and Triangles
Lesson Quiz I
1. Find mN and mP.
75°; 75°

11. 4.2 Congruence and Triangles
Lesson Quiz II 2.
105°
45°
30°
30° MN PR