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

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

Vocabulary corresponding angles corresponding sides congruent polygons Congruence Statement

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

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

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.

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.

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 + 53 + 90 = 180 mF + 143 = 180 Simplify. mF = 37° Subtract 143 from both sides.

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°.

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

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

Assignment Pg 222-224 Homework – p. 222 9-42 by 3’s Challenge - #48

Exit Slip 1. ∆ABC  ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB. Given that polygon MNOP  polygon QRST, identify the congruent corresponding part. 2. NO  ____ 3. T  ____ 4. Given: C is the midpoint of BD and AE. A  E, AB  ED Prove: ∆ABC  ∆EDC 31, 74 RS P

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