Class Greeting

Objective: The students will be able to Prove Congruence – SSS and SAS.

Proving Congruence – SSS and SAS Chapter 4 – Lesson 3 Proving Congruence – SSS and SAS

Postulate 4.1 SSS (side-side-side) If all 3 sides of one triangle are congruent to the corresponding sides of a second triangle then the triangles are congruent

G is the midpoint of both Given: G is the midpoint of both FEG HIG Prove: G 1. Given 1. Proof: Reasons Statements E H 2. Midpoint Theorem 2. 3. SSS 3. FEG HIG Example 4-1b

Write a two-column proof to prove that ABC GBC if 3. SSS 1. Given 2. Reflexive Proof: Reasons Statements 1. 2. 3. ABC GBC Example 4-1b

COORDINATE GEOMETRY Determine whether WDV MLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain. Use the Distance Formula to show that the corresponding sides are congruent. Example 4-2a

= = = = = =   = =   Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, WDV MLP by SSS. Example 4-2b

Determine whether ABC DEF for A(5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain. Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, ABC DEF by SSS. Example 4-2c

Given sides AB and CB, B is the included angle Vocabulary Included angle (between 2 given sides) The included angle between 2 given sides of a triangle is the angle whose sides are the two given sides Given sides AB and CB, B is the included angle

Postulate 4.2 SAS (side-angle-side) If 2 sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle then the two triangles are congruent

Write a flow proof. Given: Prove: QRT STR Example 4-3a

Answer: Example 4-3b

Write a flow proof. Given: . Prove: ABC ADC Example 4-3c

Proof: Midpoint Theorem Example 4-3d

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. Answer: SAS Example 4-4a

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. The third side is congruent by the Reflexive Property. So the triangles are congruent by SSS. Answer: SSS Example 4-4b

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible. a. The third side is congruent by the Reflexive Property. So the triangles are congruent by SAS. Answer: SAS Example 4-4c

b. Answer: not possible Example 4-4d

Kahoot!

Lesson Summary: Objective: The students will be able to Prove Congruence – SSS and SAS.

Preview of the Next Lesson: Objective: The students will be able to Prove Congruence – ASA, AAS and HL.

Stand Up Please