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 rigid - transformation properties

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

Step2: Analyze quadrilateral ABCD

In quadrilateral ABCD, since \(\triangle ABC\) is reflected across \(AC\) to form \(\triangle ADC\), \(AB = AD=2.7\), \(BC = CD = 3.2\), \(\angle B=\angle D = 64.3^{\circ}\), \(\angle BAC=\angle DAC\), \(\angle BCA=\angle DCA\).

Step3: Analyze quadrilateral ABCE

In quadrilateral ABCE, since \(\triangle ABC\) is rotated \(180^{\circ}\) about \(M\) to form \(\triangle CEA\), \(AB = CE = 2.7\), \(BC=AE = 3.2\), \(\angle B=\angle E=64.3^{\circ}\), \(\angle BAC=\angle ECA\), \(\angle BCA=\angle EAC\).

Answer:

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