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(Proving Congruent Triangles)

Congruence. (Proving Congruent Triangles). Proponents: Bernadine F. Culaban Leonard A. Zamora. What is congruence?. Congruence is a condition wherein all corresponding parts of a figure coincide.

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(Proving Congruent Triangles)

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  1. Congruence (Proving Congruent Triangles) Proponents: Bernadine F. Culaban Leonard A. Zamora

  2. What is congruence? Congruence is a condition wherein all corresponding parts of a figure coincide. Two polygons are congruent if they can be made to coincide. If two polygons can be made to coincide, then a. all pairs of corresponding angles are equal b. all pairs of corresponding sides are equal.

  3. SSS Congruence “If three sides of a triangle are congruent respectively to three sides of another triangle, then the triangles are congruent.” Side-Side-Side

  4. A B C M Example: Given: ∆ABC with AB=AC Prove: Angles B and C are equal Statements Reasons • AB = AC Given • BM = MC Def. of Midpoint • AM = AM Identity • ∆AMB  ∆AMC SSS • B = C CPCTE

  5. ASA Congruence A - Angle S - Included Side A - Angle “Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other.”

  6. A A X C C B B Example: Y C Given: rt. ∆ABC and rt. ∆XYZ with AC=XY and A=X Prove: rt. ∆ACB  ∆XYZ Statements Reasons • AC = XY Given • C = Y are Def. of right triangle right angles 3. C = Y All right angles are equal 4. ∆ACB  ∆XYZ ASA

  7. SAS Congruence S - Side A - Included Angle S - Side If two sides and an included angle of one triangle are congruent respectively to two sides and an included angle of another triangle, then the triangles are congruent

  8. R 1 2 N O Example: Given: RO bisects MRN, RM= RN Prove: ∆MOR  ∆NOR Statements Reasons • 1 = 2 RO bisects MRN • RO = RO Identity • RM = RN Given • ∆MOR  ∆NOR SAS M

  9. SAA Congruence S - Side A - Angle A - Angle If a side and two angles of a triangle are equal to the corresponding parts of another, then the two triangles are congruent

  10. M N 2 1 3 4 O P Example: Given: P and N are right angles 1 = 3 Prove: ∆MNO  ∆OPM Statements Reasons • P and N, rt. angles Given • P = N Right angles are equal • 1 = 3 Given • MO = MO Identity • ∆MNO  ∆OPM SAA

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