statement reason
$\overline{ac} \perp \overline{bd}$
$\angle abd \cong \angle cbd$ given
$\angle adb$ is a right angle perpendicular lines form right angles
$\angle cdb$ is a right angle perpendicular lines form right angles
$\angle adb \cong \angle cdb$ all right angles are congruent
$\overline{bd} \cong \overline{bd}$ reflexive property
$\triangle abd \cong \triangle cbd$ asa
$\overline{ab} \cong \overline{bc}$ corresponding parts of congruent triangles are congruent (cpctc)
$\triangle abc$ is an isosceles triangle select a reason...

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Accepted Answer

# Explanation:
## Step1: Recall the definition of an isosceles triangle
An isosceles triangle is defined as a triangle with at least two congruent sides (or at least two congruent angles).

## Step2: Use the result from CPCTC
From step 7, we have $\overline{AB} \cong \overline{BC}$.

## Step3: Apply the definition to $	riangle ABC$
Since $\overline{AB} \cong \overline{BC}$, triangle $ABC$ has two congruent sides. By the definition of an isosceles triangle, a triangle with two congruent sides is isosceles. So the reason is "A triangle with two congruent sides is isosceles" (or "Definition of isosceles triangle").

# Answer:
A triangle with two congruent sides is isosceles (or Definition of isosceles triangle)

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Question

Explanation:

Step1: Recall the definition of an isosceles triangle

Step2: Use the result from CPCTC

Step3: Apply the definition to $\triangle ABC$

Answer: