Question

1. match.

given: \\( \delta a b c ; \overleftrightarrow { b d } \perp \overline { a c } ; a b = b c ; a c = 8 \text { inches } \\)
what is the length of \\( \overline { a d } \\) ?
by which theorem?

Explanation:

Step1: Use the property of isosceles triangles

In an isosceles triangle \( \triangle ABC\) with \(AB = BC\) and \(BD\perp AC\), the perpendicular from the vertex (\(B\)) to the base (\(AC\)) bisects the base.

Step2: Calculate the length of \(AD\)

Since \(AC = 8\) inches and \(AD=\frac{1}{2}AC\) (by the property of isosceles triangles), then \(AD=\frac{1}{2}\times8 = 4\) inches.

Answer:

The length of \(\overline{AD}\) is \(4\) inches. By the Isosceles Triangle Theorem (the perpendicular from the vertex of an isosceles triangle to the base bisects the base).