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Proving Triangles are Congruent

Proving Triangles are Congruent. Given: ,. Prove:. There should be 5 statements with justification. Statement #1 is given. Statement # 2 is also given. Statement # 3 Reflexive Property Triangles Sharing A Side Vertical Angles Triangles With angles facing each other Mid-Point

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Proving Triangles are Congruent

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  1. Proving Triangles are Congruent • Given: , Prove: There should be 5 statements with justification • Statement #1 is given. • Statement # 2 is also given. • Statement # 3 • Reflexive Property • Triangles Sharing A Side • Vertical Angles • Triangles With angles facing each other • Mid-Point • Mid-point is given, triangles connected by a point. • Statement # 4 Congruence Postulates • SSS, SAS, AAS, ASA • Statement # 5 (CPCTC) • Congruent Parts of Congruent Triangles are Congruent Statements Justifications 1. Given • 2. Given 3. Reflexive Property 4. SAS Congruency Postulate 5. CPCTC

  2. Prove: Given: M What is given? HINT: Markings Given: N Statement Justification A What is given? HINT: Markings Given I Which Property is shown? JUSTIFY Given What congruence postulate works? Reflexive Property What can we conclude? SSS CPCTC

  3. Prove: P Statement Justification

  4. Prove: Prove:

  5. Prove: Given: B is the midpoint of N Statement Justification A Given Given (Definition of Midpoint) Vertical Angles SAS CPCTC

  6. Prove: Given: R is the midpoint of T R I S Statement Justification P Given I Given (Definition of Midpoint) Vertical Angles ASA CPCTC

  7. Prove: R Statement Justification T I P SHOW ALL YOUR WORK

  8. Prove: Statement Justification SHOW ALL YOUR WORK

  9. Prove: Prove:

  10. Prove: Prove: Prove: Prove: Given: U is the midpoint of T R

  11. Prove: T P Statement Justification I R SHOW ALL YOUR WORK

  12. In ∆ROD the & . Write the sides of the ∆ in descending order: In ∆MON the & . Write the sides of the ∆ in descending order: If two sides of a triangle re 9 and 17, which of these can not be the third side of the triangles? Explain why? 9, 18, 21, 26, 35 If two sides of a triangle re 21 and 30, which of these can not be the third side of the triangles? Explain why? 51, 10, 18, 49, 53, 12 In triangle PQR, PQ>QR & QR > RP. Which angle in triangle PQR has the smallest measure

  13. In ∆MON the & . Write the sides of the ∆ in descending order: In ∆ROD the & . Write the sides of the ∆ in descending order: If two sides of a triangle are 32 and 9, which of these can not be the third side of the triangles? Explain why? 9, 25, 28, 26, 41 If two sides of a triangle re 18 and 35, which of these can not be the third side of the triangles? Explain why? 53, 50, 18, 20, 17, 99 In triangle RST, RS>ST & ST > TR. Which angle in triangle PQR has the smallest measure

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