Question

given gk = xz and gh = xy, which statement must be true?
○ $m\angle g > m\angle x$
○ $m\angle g < m\angle x$
○ $hg = xz$
○ $hk = yz$
(images of two right triangles: triangle ghk with hypotenuse hk = 21 cm, and triangle xyz with hypotenuse yz = 26 cm, both with one leg and the other leg marked as equal with tick marks)

Explanation:

Step1: Identify triangle sides

Triangles \( \triangle GHK \) and \( \triangle XYZ \): \( GH=XY \) (marked equal), \( GK=XZ \) (marked equal), hypotenuses \( HK=21\,\text{cm} \), \( YZ=26\,\text{cm} \).

Step2: Apply Hinge Theorem

For two triangles with two equal sides, the larger included angle is opposite the longer third side. Since \( YZ > HK \), \( m\angle X > m\angle G \).

Answer:

B. \( m\angle G < m\angle X \)