4-3: Congruent Triangles Do NOW 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Page 276 16) 13 3/4° 17) 90 – 2x° 18) 33.2° 19) 162° 20) 61° 21) 48°, 48° 22) 128°, 128° 23) 15°, 60°, 105° 26) 50° 29) 36° 30) 48° 31) 32) 42° 33) 120°, 360° 34) 37.5° 35) 18° 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles 2/18/2019 12:14 AM 4-3: Congruent Triangles

Section 4-3 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us Congruent Triangles Section 4-3 Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Congruent Polygons Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. Two polygons are congruent polygons if and only if their corresponding sides are congruent. 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Example 1 Given: ∆PQR  ∆STW. Identify the congruent parts of 𝑷𝑸 and ∠𝑾 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Example 2 Given: ∆ABC  ∆DBC. Find the value of x. BCA and BCD are rt. s. BCA  BCD mBCA = mBCD (2x – 16)° = 90° 2x = 106 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Your Turn Given: ∆ABC  ∆DBC. Solve for ∆DBC. mABC + mBCA + mA = 180° mABC + 90° + 49.3° = 180° mABC + 139.3 = 180° mABC = 40.7° DBC  ABC mDBC = mABC 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Example 3 Given: YWX and YWZ are right angles. 𝒀𝑾 bisects XYZ. W is the midpoint of 𝑿𝒁 . 𝑿𝒀  𝒀𝒁 Prove: ∆XYW  ∆ZYW Statements Reasons 1) YWX and YWZ are rt. s. Given 2) YWX  YWZ Right Angle Theorem 3) YW bisects XYZ Given 4) XYW  ZYW Definition of bisector 5) W is midpoint of 𝑿𝒁 Given 6) 𝑿𝑾  𝒁𝑾 Definition of Midpoint 7) 𝒀𝑾  𝒀𝑾 Reflexive Property 8) X  Z Third s Theorem 9) 𝑿𝒀  𝒀𝒁 Given 10) ∆XYW  ∆ZYW Def. of  ∆ 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Example 4 Given: 𝑨𝑫 bisects with 𝑩𝑬 𝑨𝑫  𝑫𝑬 ; 𝑩𝑬 bisects 𝑨𝑫 . A  D . Prove: ∆ABC  ∆DEC 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Your Turn The diagonal bars across a gate give it support. Since the angle measures and the lengths of the corresponding sides are the same, the triangles are congruent. Given: PR and QT bisect each other. PQS  RTS, QP  RT Prove: ∆QPS  ∆TRS 2/18/2019 12:14 AM 4-3: Congruent Triangles

4-3: Congruent Triangles Assignment Page 234 13-19, 23-25, 31, 32 2/18/2019 12:14 AM 4-3: Congruent Triangles