Question

lesson 10: composing figures cool down: identifying side lengths and angle measures here is a diagram showing triangle abc and some transformations of triangle abc. on the left side of the diagram, triangle abc has been reflected across line ac to form quadrilateral abcd. on the right side of the diagram, triangle abc has been rotated 180 using midpoint m as a center to form quadrilateral abce. using what you know about rigid transformations, side lengths and angle measures, label as many side lengths and angle measures as you can in quadrilaterals abcd and abce.

Explanation:

Step1: Recall properties of rigid - transformations

Rigid - transformations (reflection and rotation in this case) preserve side lengths and angle measures.

Step2: Analyze quadrilateral ABCD (reflection)

Since triangle ABC is reflected across line AC to form ABCD, $AB = AD = 2.7$, $BC=CD = 3.2$, and $\angle B=\angle D = 64.3^{\circ}$, $\angle BAC=\angle DAC$, $\angle BCA=\angle DCA$.

Step3: Analyze quadrilateral ABCE (rotation)

Since triangle ABC is rotated 180° about point M to form ABCE, $AB = CE = 2.7$, $BC = AE=3.2$, $\angle B=\angle E = 64.3^{\circ}$, $\angle BAC=\angle ECA$, $\angle BCA=\angle EAC$.

Answer:

In quadrilateral ABCD: $AB = AD = 2.7$, $BC = CD = 3.2$, $\angle B=\angle D = 64.3^{\circ}$.
In quadrilateral ABCE: $AB = CE = 2.7$, $BC = AE = 3.2$, $\angle B=\angle E = 64.3^{\circ}$.