Question

quadrilateral 1 is rotated 180° clockwise about the origin, translated left 2 units, and then reflected across the y - axis to form quadrilateral 2. the angle measures of quadrilateral 1 are given below. • ( mangle a = 74^{circ} ) • ( mangle b = 124^{circ} ) • ( mangle c = 68^{circ} ) • ( mangle d = 94^{circ} ) determine if each statement is true or false. angle g has a larger measure than angle c. the measure of angle d is congruent to the measure of angle m. angle a has a smaller measure than angle g.

Explanation:

Step1: Understand the transformation

Rotating, translating, and reflecting are rigid transformations. Rigid transformations preserve the shape and size of the figure, so quadrilateral 1 and quadrilateral 2 are congruent. Congruent figures have equal corresponding angle measures.

Step2: Analyze each statement

• Statement 1: Angle G has a larger measure than angle C

Since quadrilateral 1 and 2 are congruent, \(m\angle G=m\angle A = 74^{\circ}\) (corresponding angles). Given \(m\angle C=68^{\circ}\). Since \(74^{\circ}>68^{\circ}\), this statement is true.

• Statement 2: The measure of angle D is congruent to the measure of angle M

Since quadrilateral 1 and 2 are congruent, \(m\angle M=m\angle B=124^{\circ}\) (corresponding angles) and \(m\angle D = 94^{\circ}\). Since \(94^{\circ}
eq124^{\circ}\), this statement is false.

• Statement 3: Angle A has a smaller measure than angle G

Since \(m\angle A=m\angle G = 74^{\circ}\) (corresponding angles of congruent quadrilaterals), this statement is false.

Answer:

1. True
2. False
3. False