Chapter 4: Congruent Triangles 4.2: Proving Triangles Congruent

This seems like a lot of work to prove all 6 of these criteria… We know that Δ𝑁𝐿𝑀≅Δ𝑄𝑃𝑅 if and only if… 𝑁𝐿 ≅ 𝑄𝑃 𝐿𝑀 ≅ 𝑃𝑅 𝑀𝑁 ≅ 𝑅𝑄 ∠𝑁≅∠𝑄 ∠𝐿≅∠𝑃 ∠𝑀≅∠𝑅 This seems like a lot of work to prove all 6 of these criteria…

Congruence Postulates Postulate 12: Side-Side-Side Congruence Postulate the ∆s are ≅ all 3 sides of 1 ∆ are ≅ to all 3 sides of another If then ∆𝑨𝑩𝑪≅∆𝑫𝑬𝑭 𝑨 𝑩 𝑪 𝑫 𝑬 𝑭 ₋ ₌ Postulate 13: Side-Angle-Side Congruence Postulate ₋ ₌ 𝑨 𝑩 𝑪 𝑫 𝑬 𝑭 the ∆s are ≅ ∆𝑨𝑩𝑪≅∆𝑫𝑬𝑭 If then 2 sides and the included ∠ of 1 ∆ are ≅ to that of another Postulate 14: Angle-Side-Angle Congruence Postulate If then the ∆s are ≅ ∆𝑨𝑩𝑪≅∆𝑫𝑬𝑭 2 ∠s and the included side of 1 ∆ are ≅ to that of another 𝑫 𝑬 𝑭 ₋ 𝑨 𝑩 𝑪 ₌

Answers to 4.2 Examples Remember to justify any congruency marks you add to the diagrams.

Let’s do the last 2 from the examples together.

Let’s do the last 2 from the examples together.

No! AAA is not one of our triangle congruency postulates.

Proofs Statements Reasons 3 4 Given: 𝑂𝐾 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑀𝑂𝑇, 𝐾𝑂 𝑏𝑖𝑠𝑒𝑐𝑡𝑠∠𝑀𝐾𝑇 Prove: Δ𝑀𝑂𝐾≅Δ𝑇𝑂𝐾 Statements Reasons