Question

use the following diagram for the following questions.
if ( \triangle defcong\triangle gjh ), determine each missing measure.
7 fill in the blank 1 point
df - choose your answer...
8 fill in the blank 1 point
jh - choose your answer...
9 fill in the blank 1 point
( mangle f - ) choose your answer...
10 fill in the blank 1 point
( mangle j - ) choose your answer...

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle DEF\cong\triangle GJH\), corresponding sides and angles are equal.
For side \(DF\) and \(GH\): \(DF = GH\). Given \(GH = 19m\), so \(DF=19m\).

Step2: For side \(JH\) and \(EF\)

\(JH = EF\). Given \(EF = 17m\), so \(JH = 17m\).

Step3: For angle \(\angle F\) and \(\angle H\)

\(m\angle F=m\angle H\). Given \(m\angle H = 100^{\circ}\), so \(m\angle F = 100^{\circ}\).

Step4: For angle \(\angle J\) and \(\angle E\)

The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle DEF\), \(m\angle D = 30^{\circ}\), \(m\angle F=100^{\circ}\), so \(m\angle E=180-(30 + 100)=50^{\circ}\). Then \(m\angle J=m\angle E = 50^{\circ}\).

Answer:

1. \(19m\)
2. \(17m\)
3. \(100^{\circ}\)
4. \(50^{\circ}\)