1. Splash Screen

2. Find m1.
A. 115
B. 105
C. 75
D. 65
5-Minute Check 1

3. Find m2.
A. 75
B. 72
C. 57
D. 40
5-Minute Check 2

4. Find m3.
A. 75
B. 72
C. 57
D. 40
5-Minute Check 3

5. Find m4.
A. 18
B. 28
C. 50
D. 75
5-Minute Check 4

6. Find m5.
A. 70
B. 90
C. 122
D. 140
5-Minute Check 5

7. One angle in an isosceles triangle has a measure of 80°
One angle in an isosceles triangle has a measure of 80°. What is the measure of one of the other two angles?
A. 35
B. 40
C. 50
D. 100
5-Minute Check 6

8. congruent
congruent polygons
corresponding parts
Vocabulary

9. Concept 1

10. Identify Corresponding Congruent Parts
Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.
Angles:
Sides:
Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE  RTPSQ.
Example 1

11. The support beams on the fence form congruent triangles
The support beams on the fence form congruent triangles. In the figure ΔABC  ΔDEF, which of the following congruence statements correctly identifies corresponding angles or sides? A. B. C. D.
Example 1

12. In the diagram, ΔITP  ΔNGO. Find the values of x and y.
Use Corresponding Parts of Congruent Triangles
In the diagram, ΔITP  ΔNGO. Find the values of x and y.
O  P CPCTC
mO = mP Definition of congruence
6y – 14 = 40 Substitution
Example 2

13. NG = IT Definition of congruence x – 2y = 7.5 Substitution
Use Corresponding Parts of Congruent Triangles
6y = 54 Add 14 to each side.
y = 9 Divide each side by 6.
CPCTC
NG = IT Definition of congruence
x – 2y = 7.5 Substitution
x – 2(9) = 7.5 y = 9
x – 18 = 7.5 Simplify.
x = 25.5 Add 18 to each side.
Answer: x = 25.5, y = 9
Example 2

14. In the diagram, ΔFHJ  ΔHFG. Find the values of x and y.
A. x = 4.5, y = 2.75
B. x = 2.75, y = 4.5
C. x = 1.8, y = 19
D. x = 4.5, y = 5.5
Example 2

15. Concept 2

16. ΔJIK  ΔJIH Congruent Triangles
Use the Third Angles Theorem
ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If IJK  IKJ and mIJK = 72, find mJIH.
ΔJIK  ΔJIH Congruent Triangles
mIJK + mIKJ + mJIK = 180 Triangle Angle-Sum Theorem
Example 3

17. mIJK + mIJK + mJIK = 180 Substitution
Use the Third Angles Theorem
mIJK + mIJK + mJIK = 180 Substitution
mJIK = 180 Substitution
144 + mJIK = 180 Simplify.
mJIK = 36 Subtract 144 from each side.
mJIH = 36 Third Angles Theorem
Answer: mJIH = 36
Example 3

18. TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ΔKLM  ΔNJL, KLM  KML, and mKML = 47.5, find mLNJ.
A. 85
B. 45
C. 47.5
D. 95
Example 3

19. Write a two-column proof.
Prove That Two Triangles are Congruent
Write a two-column proof.
Prove: ΔLMN  ΔPON
Example 4

20. 2. Vertical Angles Theorem
Prove That Two Triangles are Congruent
Proof:
Statements Reasons
1. Given 1.
2. LNM  PNO
2. Vertical Angles Theorem
3. M  O
3. Third Angles Theorem
4. ΔLMN  ΔPON
4. CPCTC
Example 4

21. Find the missing information in the following proof.
Prove: ΔQNP  ΔOPN
Proof:
Reasons
Statements 1.
1. Given 2.
2. Reflexive Property of Congruence
3. Q  O, NPQ  PNO
3. Given
4. _________________
4. QNP  ONP ?
5. Definition of Congruent Polygons
5. ΔQNP  ΔOPN
Example 4

22. B. Vertical Angles Theorem
A. CPCTC
B. Vertical Angles Theorem
C. Third Angles Theorem
D. Definition of Congruent Angles
Example 4

23. Concept 3