Geometry

The length of ST is 8 units. S'T'is the image of ST under a dilation with a scale factor of k. Which expression gives the length of S'T' ?

• 8-k

• 8+k

• 8/k

• 8k

△A'B'C' the image of △ABC under a dilation with a scale factor of 4, centered at the origin. If AB=8 units, what is the unit length of A'B' ?

• 2

• 32

• 12

• 4

Arianna claims that the rectangles shown below are similar, while Miguel claims that they are not similar. Whose claim is correct and why?

• Miguel is correct because the two rectangles are not oriented in the same direction.

• Arianna is correct because the four angles of the smaller rectangle are the same as the four angles of the larger rectangle.

• Arianna is correct because the smaller rectangle has side lengths that are half the size of the side lengths of the larger rectangle.

• Miguel is correct because the measures of the sides of the smaller rectangle are not proportional to the measures of the sides of the larger rectangle.

△R'S'T' is the image of △RST under a similarity transformation. Which statement BEST describes the relationship between the side lengths and angle measures of the two triangles?

• The angle measures and the side lengths are equal.

• The angle measures and the side lengths are proportional.

• The angle measures are equal, and the side lengths are proportional.

• The side lengths are equal, and the angle measures are proportional.

Look at the diagram below that shows △CAB∼△CED .

Which statement is TRUE?

• m∠DCE=24∘ and m∠E=77

• m∠D=79∘ and m∠E=77∘

• m∠D=78∘ and m∠E=78∘

• m∠D=77∘ and m∠E=79

The graph below shows triangle A and triangle B. The side lengths of triangle A are proportional to the side lengths of triangle B, and the corresponding angle measures of the two triangles are equal.

Which statement BEST describes the relationship between triangle A and triangle B?

• The triangles are similar but not congruent.

• The triangles are congruent but not similar.

• The triangles are both similar and congruent.

• The triangles are neither similar nor congruent

Omar thinks that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. To show this, he drew the figure below.Which set of transformations maps △ABC to △DEC and support Omar's thinking?

• a rotation of 180° clockwise about point C followed by a dilation with a center of point C and a scale factor of 2

• a rotation of 180° clockwise about point C followed by a dilation with a center of point C and a scale factor of 1212

  C

• a rotation of 180° counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of 3

• a rotation of 180° counter-clockwise about point C followed by a dilation with a center of point C and a scale factor of 13

A boy stands inside a shadow cast by a tree, as shown in the diagram below.

The boy knows his own height and can measure the length of his shadow as well as the length of the tree's shadow. Which postulate will allow the boy to find the height of the tree?

• AAS

• AA

• SAS

• SSS

What is the length of AC?

• 18 feet

• 9 feet

• 3 feet

• 4 feet

A lamppost is 6 feet high and casts an 8 foot shadow. At the same time of day, a flagpole near the lamppost casts a 20 foot shadow. Using the properties of similar triangles, find the height, H, of the flagpole.

• 2.4 ft

• 15 ft

• 20 ft

• 26.67 ft