Question

given △abc≅△gjk, complete the following congruency statements.
a. m∠a = ___
b. m∠k = ___
c. m∠b = ___
d. bc = ___
e. ac = ___
f. gj = ___

Explanation:

Step1: Recall congruent - triangle property

Corresponding angles of congruent triangles are equal. Since \(\triangle ABC\cong\triangle GJK\), \(\angle A\) corresponds to \(\angle G\), \(\angle B\) corresponds to \(\angle J\), and \(\angle C\) corresponds to \(\angle K\).

Step2: Find \(m\angle A\)

In \(\triangle GJK\), \(m\angle G = 52^{\circ}\), so \(m\angle A=m\angle G = 52^{\circ}\).

Step3: Find \(m\angle K\)

In \(\triangle ABC\), \(m\angle C = 39^{\circ}\), so \(m\angle K=m\angle C = 39^{\circ}\).

Step4: Find \(m\angle B\)

In \(\triangle GJK\), \(m\angle J=89^{\circ}\), so \(m\angle B=m\angle J = 89^{\circ}\).

Step5: Recall congruent - triangle property for sides

Corresponding sides of congruent triangles are equal. \(BC\) corresponds to \(JK\), \(AC\) corresponds to \(GK\), and \(AB\) corresponds to \(GJ\).

Step6: Find \(BC\)

\(BC = JK=8\) in.

Step7: Find \(AC\)

\(AC = GK = 12\) in.

Step8: Find \(GJ\)

\(GJ=AB = 5\) in.

Answer:

a. \(52^{\circ}\)
b. \(39^{\circ}\)
c. \(89^{\circ}\)
d. \(8\)
e. \(12\)
f. \(5\)