1. Chapter 4: Congruent Triangles 4.2: Proving Triangles Congruent

2. 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…

3. 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 ₌

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

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

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

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

8. Proofs Statements Reasons3 4
Given: 𝑂𝐾 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝑀𝑂𝑇, 𝐾𝑂 𝑏𝑖𝑠𝑒𝑐𝑡𝑠∠𝑀𝐾𝑇 Prove: Δ𝑀𝑂𝐾≅Δ𝑇𝑂𝐾
Statements
Reasons