Proving Triangles are Congruent (NOTES) There should be 5 statements with justification Given: 𝐴𝐶 ≅ 𝐷𝐵 , ∠𝐴𝐶𝐷≅ ∠𝐵𝐷𝐶 Prove: ∠𝐴≅∠𝐵 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) Corresponding Parts of Congruent Triangles are Congruent 𝐶 𝐵 𝐴 𝐷 Statements Justifications 1. 𝐴𝐶 ≅ 𝐷𝐵 Given 2.∠𝐴𝐶𝐷≅ ∠𝐵𝐷𝐶 Given 3. 𝐶𝐷 ≅ 𝐶𝐷 Reflexive Property 4. ∆𝐴𝐷𝐶≅∆𝐵𝐶𝐷 SAS Congruency Postulate 5. ∠𝐴≅∠𝐵 CPCTC

Prove: Given: Given: Statement Justification Given Given What is given? HINT: Markings Given: N A Statement Justification 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

Prove: 𝐴𝐷 ≅ 𝐸𝐶 Given: B is the midpoint of 𝐷𝐶 Statement Justification 𝐴𝐵 𝐸𝐵 𝐷𝐵 𝐶𝐵 Given (Definition of Midpoint) ∠𝐷𝐵𝐴 ∠𝐶𝐵𝐸 Vertical Angles ∆𝐷𝐵𝐴 ∆𝐶𝐵𝐸 SAS 𝐴𝐷 ≅ 𝐸𝐶 CPCTC

Prove: ∠𝑇≅∠𝑃 Given: R is the midpoint of 𝑆𝐼 Statement Justification ∠𝑆 ∠I 𝑆𝑅 𝐼𝑅 Given (Definition of Midpoint) ∠𝑇𝑅𝑆 ∠𝑃𝑅𝐼 Vertical Angles ∆𝑇𝑅𝑆 ∆𝑃𝑅𝐼 ASA ∠𝑇≅∠𝑃 CPCTC

Prove: ∠𝑂≅ ∠P Statement Justification

Prove: Prove: ∠𝐴≅∠𝐶 ∠𝑄≅∠𝑁

Prove: ∠𝑅≅ ∠𝑃 R Statement Justification T I P SHOW ALL YOUR WORK

Prove: ∠𝐾≅ ∠M Statement Justification SHOW ALL YOUR WORK

Prove: Prove: ∠𝐷≅∠𝐸 ∠𝐺≅∠I

Prove: Prove: Prove: Prove: ∠𝑂≅∠𝑃 ∠𝐿≅∠𝐽 ∠𝑋≅∠𝑅 ∠𝑆≅∠𝑊 Given: U is the midpoint of 𝑆𝑊 T R I

Prove: ∠𝑇≅ ∠𝑅 T P Statement Justification I R SHOW ALL YOUR WORK

In ∆MON the 𝑚∠𝑀 53° & 𝑚∠O 90°. Write the sides of the ∆ in descending order: In ∆ROD the 𝑚∠𝑅 46° & 𝑚∠O 95°. 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

In ∆MON the 𝑚∠𝑀 60° & 𝑚∠O 82°. Write the sides of the ∆ in descending order: In ∆ROD the 𝑚∠𝑅 63° & 𝑚∠O 105°. 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