Question

finding unknown measures of congruent figures
in the diagram, △ghj≅△stu.
what are the missing measures in the diagram?
m∠j=
m∠t=
m∠g=
st=
hj=

Explanation:

Step1: Recall congruent - triangle property

Corresponding angles and sides of congruent triangles are equal.

Step2: Find \(m\angle J\)

In \(\triangle GHJ\), assume the un - labeled angle at \(G\) and \(J\) are equal (isosceles - like property from the tick marks). Using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle), if one angle is \(67^{\circ}\), then \(m\angle J=\frac{180 - 67}{2}=56.5^{\circ}\). Since \(\triangle GHJ\cong\triangle STU\), \(m\angle J = 56.5^{\circ}\).

Step3: Find \(m\angle T\)

\(m\angle T\) corresponds to \(m\angle H\), so \(m\angle T = 67^{\circ}\).

Step4: Find \(m\angle G\)

\(m\angle G\) corresponds to \(m\angle S\). Since \(m\angle J = 56.5^{\circ}\), \(m\angle G=56.5^{\circ}\).

Step5: Find \(ST\)

\(ST\) corresponds to \(GH\), so \(ST = 5\mathrm{cm}\).

Step6: Find \(HJ\)

\(HJ\) corresponds to \(TU\), so \(HJ = 3.7\mathrm{cm}\).

Answer:

\(m\angle J = 56.5^{\circ}\), \(m\angle T = 67^{\circ}\), \(m\angle G = 56.5^{\circ}\), \(ST = 5\mathrm{cm}\), \(HJ = 3.7\mathrm{cm}\)