1. FG, GH, FH, F, G, H Warm Up 1. Name all sides and angles of ∆FGH.
2. What is true about K and L? Why?
3. What does it mean for two segments to be congruent?
FG, GH, FH, F, G, H
 ;Third s Thm.
They have the same length.

2. Objectives Use properties of congruent triangles.
Prove triangles congruent by using the definition of congruence.

3. The Idea of a Congruence
Two geometric figures with exactly the same size and shape. A C B D E F
Each triangle is made up of six parts:
3 sides and 3 angles

4. Corresponding Parts
If all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. B A C
AB  DE
BC  EF
AC  DF
 A   D
 B   E
 C   F
ABC   DEF E D F

6. For example, P and Q are consecutive vertices. P and S are not.
Two vertices that are the endpoints of a side are called consecutive vertices.
For example, P and Q are consecutive vertices. P and S are not.
Helpful Hint P Q S

7. To name a polygon, write the vertices in consecutive order.
In a congruence statement, the order of the vertices indicates the corresponding parts.  so the order MATTERS!

8. When you write a statement such as ABC  DEF, you are also stating which parts are congruent.
Helpful Hint

9. Identify all pairs of corresponding congruent parts.
Example 1: Naming Congruent Corresponding Parts
Given: ∆PQR  ∆STW
Identify all pairs of corresponding congruent parts.
Angles: P  S, Q  T, R  W
Sides: PQ  ST, QR  TW, PR  SW

10. CPCTC Corresponding Parts of Congruent Triangles are Congruent.

11. Congruence Transformations
Congruency amongst triangles does not change when you…
slide (translation),
Turn (rotation),
or flip (reflection)
… the triangles.

12. EXAMPLE 1
Identify congruent parts
Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts.

13. Complete each congruence statement.

14. Complete each congruence statement.

17. Write a congruence statement.

18. Write a congruence statement.

19. Given ΔBCD = ΔRST, m C = 57, m R = 64, m D = 5x + 4. Find x and m T.
Given ΔQRS = ΔLMN, RS = 8, QR=14, QS=10, MN = 3x – 25. Find x.

20. Given ΔBCD = ΔRST, m C = 57, m R = 64, m D = 5x + 4. Find x and m T.
Given ΔQRS = ΔLMN, RS = 8, QR=14, QS=10, MN = 3x – 25. Find x.

21. Name the corresponding angles and sides if ΔBCD = ΔEFG.
Given ΔCAT = ΔDOG, CA=14, AT=18, TC=21 and
DG=2x+7, find the value of x.

22. Name the corresponding angles and sides if ΔBCD = ΔEFG.
Given ΔCAT = ΔDOG, CA=14, AT=18, TC=21 and
DG=2x+7, find the value of x.

23. Given: ∆ABC  ∆DBC. BCA and BCD are rt. s. Def. of  lines.
Example 2A: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find the value of x. Find mDBC.
BCA and BCD are rt. s.
Def. of  lines.
BCA  BCD
Rt.   Thm.
mBCA = mBCD
Def. of  s
Substitute values for mBCA and mBCD.
(2x – 16)° = 90°
2x = 106
Add 16 to both sides.
x = 53
Divide both sides by 2.

24. Given: ∆ABC  ∆DBC. ∆ Sum Thm. mABC + mBCA + mA = 180°
Example 2B: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find mDBC.
mABC + mBCA + mA = 180°
∆ Sum Thm.
mABC = 180
Substitute values for mBCA and mA.
mABC = 180
Simplify.
mABC = 40.7
Subtract from both sides.
DBC  ABC
Corr. s of  ∆s are  .
mDBC = mABC
Def. of  s.
mDBC  40.7°
Trans. Prop. of =

25. Given: ∆ABC  ∆DEF AB  DE Corr. sides of  ∆s are . AB = DE
Check It Out! Example 3a
Given: ∆ABC  ∆DEF
Find the value of x. Find mF.
AB  DE
Corr. sides of  ∆s are .
AB = DE
Def. of  parts.
Substitute values for AB and DE.
2x – 2 = 6
2x = 8
Add 2 to both sides.
x = 4
Divide both sides by 2.

26. Given: ∆ABC  ∆DEF ∆ Sum Thm. mEFD + mDEF + mFDE = 180° ABC  DEF
Check It Out! Example 3b
Given: ∆ABC  ∆DEF
Find mF.
∆ Sum Thm.
mEFD + mDEF + mFDE = 180°
ABC  DEF
Corr. s of  ∆ are .
mABC = mDEF
Def. of  s.
mDEF = 53°
Transitive Prop. of =.
Substitute values for mDEF and mFDE.
mEFD = 180
mF = 180
Simplify.
mF = 37°
Subtract 143 from both sides.

27. 1. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB.
Lesson Quiz
1. ∆ABC  ∆JKL and AB = 2x JK = 4x – 50. Find x and AB.
Given that polygon MNOP  polygon QRST, identify the congruent corresponding part.
2. NO  ____ T  ____