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The image contains a mathematical problem in Japanese. Here's a translation and breakdown of the content:

### Problem Statement:
1. \( ABC \) is an isosceles triangle with \( AB = AC \). \( D \) is the midpoint of side \( BC \), and \( M \) is the midpoint of side \( AD \).
2. Prove that the line \( BM \) is perpendicular to the line \( AM \).

### Tasks:
1. **Proof that the angle between \( BM \) and \( AM \) is a right angle.**
2. **Demonstrate that the length of \( AM \) equals the length of \( BM \).**
3. **Show that the angle \( \angle ABM \) is equal to the angle \( \angle BAM \).**

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ABCは二等辺三角形である。AB = ACである。Dは辺BCの中点で、Mは辺ADの中点である。線BMが線AMに垂直であることを証明せよ。

This problem involves proving that the line BM is perpendicular to line AM in an isosceles triangle where D and M are midpoints. The solution requires knowledge of geometric properties, including the midpoint formula and the Pythagorean theorem. Suitable for Grades 9-10.

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