Question

1. if △wxy≅△hji, complete each part. a) ji = b) jh = c) m∠w = d) m∠j = e) m∠i =

Explanation:

Step1: Recall congruent - triangle properties

If $\triangle WXY\cong\triangle HJI$, corresponding parts are equal.

Step2: Find corresponding sides and angles

• a) Corresponding sides: $JI = XY$. Given $XY = 16$ m, so $JI=16$ m.
• b) Corresponding sides: $JH = WX$. Given $WX = 15$ m, so $JH = 15$ m.
• c) Corresponding angles: $\angle W=\angle H$. Given $\angle H = 37^{\circ}$, so $m\angle W=37^{\circ}$.
• d) Corresponding angles: $\angle J=\angle X$. Given $\angle X = 114^{\circ}$, so $m\angle J = 114^{\circ}$.
• e) Use angle - sum property of a triangle

In $\triangle HJI$, we know that the sum of interior angles of a triangle is $180^{\circ}$. Let $\angle H = 37^{\circ}$, $\angle J=114^{\circ}$. Then $m\angle I=180-(37 + 114)=29^{\circ}$.

Answer:

a) $JI = 16$ m
b) $JH = 15$ m
c) $m\angle W=37^{\circ}$
d) $m\angle J = 114^{\circ}$
e) $m\angle I = 29^{\circ}$