Congruence and Similarity in Two-Dimensional Figures

Tell whether the two figures are similar. Explain your reasoning.

• Yes, similar because they are the same shape and side lengths are proportional.

• No, not similar because they are the same shape, but side lengths are not proportional.

• Yes, same shape

• No, different sizes

Solve for X.

• 2 ft

• 3 ft

• 4 ft

• 6 ft

A pentagon graphed on a coordinate plane underwent a rotation about the origin, a reflection across the y–axis, a translation down, and a dilation with a scale factor of 3 from its center to produce another pentagon. Which of these statements is true about the original pentagon and the new pentagon?

• They are similar.

• They may or may not be similar, depending on the number of units translated.

• They may or may not be similar, depending on the number of degrees rotated.

• They are not similar.

If ∆LMK ≅ ∆LMT, then
∠K ≅ ____

• T

• ∠T

• ∠M

• ∠L

Line segment AB is reflected across the y-axis to form segment CD. Then, segment CD is rotated 180 degrees clockwise to form segment EF. Which statement is TRUE about this transformation?

• Line segment EF is the same length as line segment AB.

• Line segment EF is longer than line segment CD.

• Line segment EF is shorter than line segment AB.

• Line segment CD is shorter than line segment AB.

What is the similarity statement for the triangle pair?

• ΔXYZ is similar to ΔNEW

• ΔXZY is similar to ΔNWE

• ΔZYX is similar to ΔENW

• ΔYZX is similar to ΔNWE

The pair of figures is similar. Find the missing side.

• x = 20

• x = 12

• x = 5

• x = 4

Calculate the value of the scale factor between the 2 triangles

• 2.5

• 3

• 3.5

• 4

Given that the two triangles are similar,

find the value of X and Y.

• X=2.5 and Y=6.5

• X=6.5 and Y=2.5

• X=3 and Y=7

• X=2 and Y= 5