1. FG, GH, FH, F, G, H Entry Task
1. Name all sides and angles of ∆FGH.
FG, GH, FH, F, G, H

2. I can recognize congruent figures and their corresponding parts.
Learning Target:
I can recognize congruent figures and their corresponding parts.
Success Criteria: I can label congruent figures and their corresponding parts

3. Vocabulary
corresponding angles
corresponding sides
congruent polygons
Congruence Statement

6. Naming Polygons
To name a polygon, write the vertices in consecutive order.
ORDER MATTERS!
In a congruence statement, the order of the vertices indicates the corresponding parts. X A Y B C Z

7. 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

8. Example 2A: Using Corresponding Parts of Congruent Triangles
Given: ∆ABC  ∆DBC.
Find the value of x.
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.

9. Check It Out! Example 2a Given: ∆ABC  ∆DEF Find the value of x.
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.

10. Check It Out! Example 2b 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.

12. Example 4: 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°.

13. Check It Out! Example 3
Given: AD bisects BE.
BE bisects AD.
AB  DE, A  D
Prove: ∆ABC  ∆DEC

14. 1. A  D 1. Given 2. BCA  DCE 2. Vertical s are .
Statements
Reasons
1. A  D
1. Given
2. BCA  DCE
2. Vertical s are .
3. ABC  DEC
3. Third s Thm.
4. Given
4. AB  DE
BE bisects AD
5. AD bisects BE,
5. Given
6. BC  EC,
AC  DC
6. Def. of bisector
7. ∆ABC  ∆DEC
7. Def. of  ∆s

15. Assignment Pg
Homework – p by 3’s Challenge - #48

16. Exit Slip
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  ____
4. Given: C is the midpoint of BD and AE.
A  E, AB  ED
Prove: ∆ABC  ∆EDC
31, 74 RS P

17. 7. Def. of  ∆s
7. ABC  EDC
6. Third s Thm.
6. B  D
5. Vert. s Thm.
5. ACB  ECD
4. Given
4. AB  ED
3. Def. of mdpt.
3. AC  EC; BC  DC
2. Given
2. C is mdpt. of BD and AE
1. Given
1. A  E
Reasons
Statements