Similar Triangles on the Coordinate Plane

Which transformation(s) create(s) similar figures?

• Dilation

• Translation, Reflection, and Rotation

• Translation and Reflection

• Reflection and Rotation

Two objects that are the same shape but not the same size are _______.

• Congruent

• Vertical

• Similar

• Complementary 

Two similar right triangles are shown in the coordinate plane. Point P lies on line segment PR. Which statement best compares the slope of PQ to the slope of PR.

• PQ and PR have the same length, so the slopes must be equal.

• The lengths of the corresponding legs of the two triangles are proportional because they are similar, so the slopes must be equal.

• The horizontal distance from P to Q is 2 units, but the vertical distance is 4 units, so the slopes can't be equal.

• The short leg of the large triangle is the same length as the long leg of the small triangle, so the slopes cannot be equal.

These are ​ (a)   triangles because they have the ​ (b)   shape but ​ (c)   size. The sides are ​ (d)   .

• similar

• congruent

• same

• different

• proportional

Find the length of DF.

Find the value of x. Type only the value, not x =

Mathematical Equivalence

OFF

Solve.

c

d

f

9 in.

10 in

15 in.

similar

different

congruent/equal

Answer explanation

• are

• are not

• congruent

• proportional

Based on the diagram below, find the length of TR.

• Reflection

• Rotation

• Translation

• Dilation