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Mastering Triangle Proofs: Congruent Triangles & Properties

Learn to use congruent triangles in proofs. Apply properties of isosceles, equilateral, and right triangles to prove congruency. Understanding CPCTC and triangle properties is key. Prepare for quiz and test in a structured manner.

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Mastering Triangle Proofs: Congruent Triangles & Properties

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  1. Game Plan: Today I will be able to use congruent triangles to plan and write proofs. Today I will be able to apply properties of isosceles, equilateral & right triangles to determine measures and prove congruent triangles. Warm-up: Given PQSWXY. List all corresponding parts of the congruent triangles. HMWK:p. 232, #s 4 – 18 p. 240, #17 – 25, 33, 34 (two proofs)

  2. CPCTC • CPCTC: Corresponding Parts of Congruent Triangles are Congruent. why? … In order to have congruent triangles all corresponding parts of the triangle must be congruent. so …

  3. Proofs

  4. Proofs

  5. Proofs

  6. Game Plan: Today I will be able to apply properties of isosceles, equilateral & right triangles to determine measures and prove congruent triangles. Warm-up: How many acute, obtuse, and right angles does each triangle have? 1. Acute triangle 2. Right triangle 3. Obtuse triangle 4. Equilateral triangle HMWK:p. 240, #17 – 25, 33, 34 (two proofs)

  7. Remember Isosceles Triangle Right Triangle

  8. Isosceles Triangles Base Angle Thm: If two sides of a triangle are congruent, then the angles opposite them are congruent. Converse Base Angle Thm: If two angles of a triangle are congruent, then the sides opposite them are congruent.

  9. Equilateral Triangles Corollary: If a triangle is equilateral, then it is equiangular. Corollary: If a triangle is equiangular, then it is equilateral.

  10. Right Triangles Hypotenuse-Leg (HL) Thm: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

  11. Looking at … • Quiz 4.1 – 4.1 on Friday • Test on Chapter 4 next Tuesday. Wrap-Up We now have five different methods to prove triangles are congruent. List all 5 ways. SSS, SAS, ASA, AAS, HL

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