Question

1. if $\triangle wxycong\triangle hij$, complete each part.

a) $ji=$_____
b) $jh=$_____
c) $mangle w=$_____
d) $mangle j=$_____
e) $mangle i=$_____

Explanation:

Step1: Use the property of congruent triangles

When \(\triangle WXY\cong\triangle HIJ\), corresponding sides and corresponding angles are equal.

Step2: Find \(JI\)

Since \(JI\) corresponds to \(XY\), and \(XY = 16m\), so \(JI=16m\).

Step3: Find \(JH\)

Since \(JH\) corresponds to \(WX\), and \(WX = 15m\), so \(JH = 15m\).

Step4: Find \(m\angle W\)

Since \(\angle W\) corresponds to \(\angle H\), and \(m\angle H=37^{\circ}\), so \(m\angle W = 37^{\circ}\).

Step5: Find \(m\angle J\)

Since \(\angle J\) corresponds to \(\angle X\), and \(m\angle X=114^{\circ}\), so \(m\angle J=114^{\circ}\).

Step6: Find \(m\angle I\)

The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle WXY\), \(m\angle Y=180-(114 + 37)=29^{\circ}\). Since \(\angle I\) corresponds to \(\angle Y\), so \(m\angle I = 29^{\circ}\).

Answer:

a) \(16m\)
b) \(15m\)
c) \(37^{\circ}\)
d) \(114^{\circ}\)
e) \(29^{\circ}\)