in exercises 1 - 4, complete the statement. state which theorem you used. example 1
1. if $ \overline { a e } \cong \overline { d e } $, then $ \angle $____$ \cong \angle $____.
2. if $ \overline { a b } \cong \overline { e b } $, then $ \angle $____$ \cong \angle $____.
3. if $ \angle d \cong \angle c e d $, then ____$ \cong $____.
4. if $ \angle e b c \cong \angle e c b $, then ____$ \cong $____.

Question

Accepted Answer

# Explanation:
## Step1: Recall the Isosceles Triangle Theorem
The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are congruent. Conversely, if two angles of a triangle are congruent, then the sides opposite those angles are congruent.
## Step2: Apply the theorem to each problem
- **Problem 1**:
Since $ \overline{AE}\cong\overline{DE} $, in $ \triangle AED $, by the Isosceles Triangle Theorem, the angles opposite these sides ($ \angle A $ and $ \angle D $) are congruent. So $ \angle A\cong\angle D $.
- **Problem 2**:
Since $ \overline{AB}\cong\overline{EB} $, in $ \triangle ABE $, by the Isosceles Triangle Theorem, the angles opposite these sides ($ \angle AEB $ and $ \angle A $) are congruent. So $ \angle A\cong\angle AEB $.
- **Problem 3**:
Since $ \angle D\cong\angle CED $, in $ \triangle CED $, by the Isosceles Triangle Theorem (converse), the sides opposite these angles ($ \overline{EC} $ and $ \overline{CD} $) are congruent. So $ \overline{EC}\cong\overline{CD} $.
- **Problem 4**:
Since $ \angle EBC\cong\angle ECB $, in $ \triangle EBC $, by the Isosceles Triangle Theorem (converse), the sides opposite these angles ($ \overline{EB} $ and $ \overline{EC} $) are congruent. So $ \overline{EB}\cong\overline{EC} $.

# Answer:
1. $ \angle A\cong\angle D $ (Isosceles Triangle Theorem)
2. $ \angle A\cong\angle AEB $ (Isosceles Triangle Theorem)
3. $ \overline{EC}\cong\overline{CD} $ (Converse of Isosceles Triangle Theorem)
4. $ \overline{EB}\cong\overline{EC} $ (Converse of Isosceles Triangle Theorem)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the Isosceles Triangle Theorem

Step2: Apply the theorem to each problem

Answer: