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Objectives: Use congruence of triangles to conclude congruence of corresponding parts.

4.4 Using Triangle Congruence. Objectives: Use congruence of triangles to conclude congruence of corresponding parts. Develop and use the Isosceles Triangle Theorem. Warm-Up:. Reasons. Statements. Given: ABCD is a rectangle. Prove: Δ ABC & Δ CDA are by ASA. A. B. C.

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Objectives: Use congruence of triangles to conclude congruence of corresponding parts.

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  1. 4.4 Using Triangle Congruence Objectives: Use congruence of triangles to conclude congruence of corresponding parts. Develop and use the Isosceles Triangle Theorem Warm-Up: Reasons Statements Given: ABCD is a rectangle. Prove: ΔABC & ΔCDA are by ASA A B C D

  2. VERTEX ANGLE An isoscelestriangle is a triangle with at least two congruent sides. The two congruent sides are known as the legs of the triangle, and the remaining side is known as the base. The angles whose vertices are the endpoints of the base are known as base angles, and the angle opposite the base is known as the vertex angle. LEGS BASE ANGLES BASE

  3. Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of the Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

  4. Corollary: A corollary of a theorem is an additional theorem that can easily be derived from the original theorem. Once the theorem is known, the corollary should seem obvious. A corollary can be used as a reason in a proof, just like a theorem or postulate.

  5. Corollary: The measure of each angle of an equilateral triangle is . Corollary: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

  6. Examples: • B • What is the length of BA? • C • A • X • What is the measure of <Y? • Y • Z

  7. Examples: • Find each indicated measure. • X • <X=___ • K • KL=___ • <Z=___ • M • Y • L • Z • E • F • Q • <F=___ • QR=___ • G • P • R

  8. Examples: • Find each indicated measure. • B • H • <ABD=___ • GH=___ • J • F • C • A • D • G • Y • <X=___ • X • Z

  9. Examples: • Find each indicated measure. • <T=___ • U • 8x • 6x • T • V

  10. Examples: • Find each indicated measure. • D • F • <F=___ • <E=___ • E • If EF = 3x-12 then ED = ___

  11. Examples: • Find each indicated measure. • X • W • XZ=___ • Y • Z

  12. Examples: • Find each indicated measure. • L • <N=___ • N • M

  13. Examples: • Find each indicated measure. • y=___ • x=___ • B • AC=___ • BC=___ • <A=___ • 8 • 3x-y • A • x+3y+2 • C

  14. Homework: • Practice Worksheet

  15. Recall that the PolygonCongruence Postulate states that if two triangles are congruent then their corresponding parts are congruent. E B If ∆ABC ∆DEF then: D A F C This idea is often stated in the following form: Corresponding Parts of Congruent Triangles are Congruent, abbreviated as CPCTC.

  16. Given: -------- ------- • Prove: ---------- • REASONS • STATEMENTS

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