Question

1. given ( \triangle bcmcong\triangle zyr ), find each missing measure.

a) ( cm=)
b) ( bm=)
c) ( yz=)
d) ( mangle b=)
e) ( mangle m=)
f) ( mangle y=)

Explanation:

Step1: Use the property of congruent triangles (corresponding sides are equal)

Since \(\triangle BCM\cong\triangle ZYR\), \(CM = RY\). From the figure, \(RY = 11m\), so \(CM=11m\).

Step2: Use the property of congruent triangles (corresponding sides are equal)

\(BM = RZ\). From the figure, \(RZ = 15m\), so \(BM = 15m\).

Step3: Use the property of congruent triangles (corresponding sides are equal)

\(YZ=BC\). From the figure, \(BC = 8m\), so \(YZ = 8m\).

Step4: Use the property of congruent triangles (corresponding angles are equal)

\(m\angle B=m\angle Z\). From the figure, \(m\angle Z = 45^{\circ}\), so \(m\angle B=45^{\circ}\).

Step5: Use the property of congruent triangles (corresponding angles are equal)

\(m\angle M=m\angle R\). The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle ZYR\), \(m\angle R=180^{\circ}-(45^{\circ}+m\angle Y)\). First find \(m\angle Y\). Since \(m\angle Y=m\angle C\) (corresponding angles of congruent triangles) and \(m\angle C = 103^{\circ}\). Then \(m\angle M=m\angle R=180^{\circ}-(45^{\circ}+ 103^{\circ})=32^{\circ}\).

Step6: Use the property of congruent triangles (corresponding angles are equal)

\(m\angle Y=m\angle C\). From the figure, \(m\angle C = 103^{\circ}\), so \(m\angle Y=103^{\circ}\).

Answer:

a) \(CM = 11m\)
b) \(BM = 15m\)
c) \(YZ = 8m\)
d) \(m\angle B=45^{\circ}\)
e) \(m\angle M = 32^{\circ}\)
f) \(m\angle Y=103^{\circ}\)