Question

look at this diagram:
diagram of triangle hij
which diagram shows δhij rotated 45° counterclockwise about i?
diagrams of rotated triangles

Explanation:

Step1: Recall Rotation Rules

A rotation about a point \( I \) means \( I \) stays fixed. A \( 45^\circ \) counterclockwise rotation will rotate segments \( IH \) and \( IJ \) \( 45^\circ \) counterclockwise around \( I \).

Step2: Analyze Each Diagram

• For the first (blue) diagram: Check if \( I \) is fixed, and the angles of \( IH' \) and \( IJ' \) relative to \( IH \) and \( IJ \) are \( 45^\circ \) counterclockwise. The blue triangle has \( I \) fixed, and the orientation change (counterclockwise \( 45^\circ \)) matches the rotation of \( \triangle HIJ \) about \( I \).
• For the lower diagram: The position of \( I \) seems altered or the rotation angle/orientation doesn't match \( 45^\circ \) counterclockwise about \( I \).

Answer:

The diagram with the blue triangle (the first one shown with \( H' \), \( I \), \( J' \))