Question

1. if ( \triangle wxy cong \triangle hji ), complete each part,

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

Explanation:

Step1: Identify corresponding parts

Since \(\triangle WXY\cong\triangle HJI\), corresponding sides and angles are equal.

• For side \(JI\), it corresponds to \(XY\). So \(JI = XY\).
• For side \(JH\), it corresponds to \(WX\). So \(JH=WX\).
• For \(\angle W\), it corresponds to \(\angle H\). So \(m\angle W = m\angle H\).
• For \(\angle J\), it corresponds to \(\angle X\). So \(m\angle J=m\angle X\).
• For \(\angle I\), use the angle - sum property of a triangle (\(180^{\circ}\)). First find \(m\angle I\) as \(180-(m\angle H + m\angle J)\)

Step2: Substitute values

• \(XY = 16m\), so \(JI=16m\)
• \(WX = 15m\), so \(JH = 15m\)
• \(m\angle H=37^{\circ}\), so \(m\angle W = 37^{\circ}\)
• \(m\angle X = 114^{\circ}\), so \(m\angle J=114^{\circ}\)
• \(m\angle I=180-(37 + 114)=29^{\circ}\)

Answer:

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