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Transcript

4-4 Congruent Triangles Objectives: G.SRT.5: Use congruence and similarity criteria for triangles to solve problems and prove relationships in geometric figures. For the Board: You will be able to prove triangles congruent by using the definition of congruent triangles. J Bell Work: 1. Name all sides and angles of ΔFGH. 2. What is true about <K and <L? Why? M I K N L 3. What does it mean for two segments to be congruent? Anticipatory Set: Geometric figures are congruent if they have the same size and shape. The shape of a triangle is determined by the measures of its angles, therefore congruent triangles have congruent corresponding angles. The size of a triangle is determined by the lengths of its sides, therefore congruent triangles have congruent corresponding sides. Definition of Congruent Triangles Two triangles are congruent if and only if all six parts of one triangle (three sides and three angles) are congruent to the six corresponding parts on another triangle. H When stating the congruence it is customary to use the correspondence. Open the book to page 239 and read example 1. Example: Given ΔXYZ ΔHJK identify all pairs of congruent corresponding parts. XY HJ, YZ JK, XZ HK, <X <H, <Y <J, <Z <K Y X K Z J White Board Activity: Practice: Given polygon LMNP polygon EFGH, identify all pairs of corresponding congruent parts. LM EF, MN FG, NP GH, PL HE, <L <E, <M <F, <N <G, <P <H Open the book to page 240 and read example 2. Example: Given ΔABC ΔDBC. a. Find x. 2x – 16 = 90 2x = 106 x = 53° b. Find m<DBC. 90 – 49.3 = 40.7° A 49.3° B (2x – 16)° C D White Board Activity: Practice: Given ΔABC ΔXYZ. a. Find x. 5x – 12 = 53 5x = 65 x = 13 X B b. Find y. 4y + 15 = 75 4y = 60 y = 15 4y + 15 C 75 Y 53° X W Reasons 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Given Right Angle Theorem Given Definition of angle bisector Third Angle Theorem Given Definition of midpoint Given Reflexive Property of Congruence Definition of Congruent Triangles Assessment: Question student pairs. Independent Practice: Text: pgs. 242 – 243 prob. 3 – 10 , 13 – 18, 23 – 25. For a Grade: Text: pgs. 242 – 243 prob. 14, 18, 24. A Z Y Read example 3 on page 240. Practice 3: Given: <YWX and <YWZ are right angles. YW bisects <XYZ. W is the midpoint of XZ. XY YZ Prove: ΔYXW ΔYZW Statements 1. <YWX and <YWZ are right angles 2. <YWX <YWZ 3. YW bisects <XYZ 4. <XYW <ZYW 5. <X <Z 6. W is the midpoint of XZ 7. XW ZW 8. XY YZ 9. YW YW 10. ΔYXW ΔYZW (5x – 12)° Z