Parallel Lines & Transversals

Suppose that on a coordinate plane a hexagon is reflected across the x-axis. Compare the area of the original hexagon to the area of the transformed figure. Justify your answer.

• The areas may or may not be the same because the scale is not given.

• The areas are equal. A reflection is a rigid transformation, which does not change the size of the original hexagon. Therefore, the area is preserved.

• The area of the original hexagon is greater than the transformed figure. A reflection decreases the size of the original polygon. Therefore, the area is not preserved.

• The area of the transformed hexagon is greater than the original figure. A reflection increases the size of the original polygon. Therefore, the area is not preserved.

Triangle ABC has been dilated to triangle A'B'C'. Which factor was used

• 1

• 2

• 3

• 4

The coordinates of a rectangle are (4, 0), (8, 0), (4, 10) and (8, 10). Which transformation results in a reduction in the size of a rectangle?

• The rectangle reflects across the y-axis

• The rectangle undergoes a dilation by a scale factor of 2.

• The rectangle translates 3 units to the left and 6 units up

• The rectangle undergoes a dilation by a scale factor of 0.5.

What is true of angles c and d?

• The two angles are equal.

• The two angles are both 90°

• The two angles are supplementary.

• The two angles are complementary.

∠a and ∠e are ______ angles.

• perpendicular

• corresponding

• complementary

• alternate interior

Which pair of angles are congruent?

• 1 and 8

• 4 and 6

• 5 and 6

• 1 and 7

If Kite ABCD is reflected across the x-axis, what are the resulting coordinates of point A?

If m∠A =91° and m∠B = 40°, find m∠1.

• 89°

• 122°

• 131°

• 140°

Identify the reflection rule on a coordinate plane that verifies that triangle A(-1,7), B(6,5), C(-2,2) and A'(-1,-7), B'(6,-5), C'(-2,-2) triangle are congruent when reflected over the x-axis.

• (x, y) → (-x, -y)

• (x, y) → (x, -y)

• (x, y) → (-x, y)

• the triangles are not congruent

The vertices of ΔABC are (-2,0), (-2, 3), and (-5, 1). T(x,y) = (x + 1, 3y) represents the transformation of the triangle. What are the coordinates of the vertices for ΔA'B'C'? Are the pre-image and image congruent? Justify your answer.

• (0,-1),(9,1),(3,-4); The triangles are congruent because all transformations result in congruent figures.

• (1,0),(1,9),(-4, 3); The triangles are not congruent because ΔA'B'C' is a reflection of ΔABC.

• (-1,3),(-1,3),(-4,3); The triangles are congruent because the same transformation was performed on each vertex.

• (-1,0),(-1,9),(-4,3); The triangles are not congruent because 3y is a dilation which increases the size of ΔA'B'C'.