4.7 Notes Geometry – Learning Target 4

Isosceles ∆:

Equilateral ∆:

Legs:

Vertex Angle:

Base:

Base Angles:

Theorem 4.7 – Base Angles Theorem:

If two sides of a triangle are congruent, then the angles opposite them are congruent.

If AB ≅ AC, then ∠B ≅ ∠C.

Proof:

Given: JK ≅ JL, M is the midpoint of KL

Prove: ∠K ≅ ∠L

Statements Reasons 1. M is the midpoint of KL 1. 2. Draw JM 2. Two points determine a line (drawn) 3. MK ≅ ML 3. 4. JK ≅ JL 4. Given 5. JM ≅ JM 5. 6. ∆JMK ≅ ΔJML 6. 7. ∠K ≅ ∠L 7. Corresponding Parts of ≅ ∆ are ≅.

Find the value of x, y or both: a. b. c.

d. e. f.

Theorem 4.8 – Converse of Base Angles Theorem:

If two angles of a triangle are congruent, then the sides opposite them are congruent.

If ∠B ≅ ∠C, then AB ≅ AC.

Example (applying Angle Base Theorem):

In ∆DEF, DE ≅ DF. Name two congruent angles:

𝐃𝐄 ≅ 𝐃𝐅 means that ∠____ ≅ ∠____

Example (applying Converse of Angle Base Theorem):

∠KHJ ≅ ∠KJH means that ____ ≅ ____

Corollary to Base Angles Theorem

If a triangle is equilateral, then it is ________________________.

Corollary to Converse of Base Angles Theorem

If a triangle is equiangular, then it is ________________________.

Example:

Corollary to BAT: If AB ≅ BC ≅ CA, then ∠A ≅ ∠B ≅ ∠C

Corollary to CBAT: If ∠A ≅ ∠B ≅ ∠C, then AB ≅ BC ≅ CA