Q#LEARN

Which sequence of transformations can be performed on triangle ABC to map it onto triangle A′B′C′?  Select all that apply.

• Dilate with scale Dilate with scale factor 2 and center A; rotate 90 degrees clockwise about point A; translate 11 units up and 6 units to the right to map point A onto point A′.

• Dilate with scale factor 12 and center A; rotate 90 degrees counterclockwise about point A; translate 6 units to the left and 11 units down to map point C onto point C′.

• Dilate with scale factor 2 and center A; rotate 90 degrees counterclockwise about point A; translate 11 units up and 6 units to the right to map point B onto point B′.

• Dilate with scale factor 2 and center A; rotate 90 degrees counterclockwise about point A; translate 11 units up and 6 units to the right to map point B onto point B′.

Which statement about △ABC and △A′B′C′ is true?

• △ABC is similar to △A′B′C′ because the lengths of the corresponding sides in proportion.

• △ABC is similar to △A′B′C′ because one triangle is smaller than the other triangle.

• △ABC is not similar to △A′B′C' because the lengths of the corresponding sides are not in proportion.

• △ABC is not similar to △A′B′C′ because one triangle cannot be obtained from the other with only a translation.

What information is needed to show △ABC∼△A′B′C′?  Type your answers in... If the measure of angle B′ is 35 degrees, then the triangles ______ similar.

What information is needed to show △ABC∼△A′B′C′?  It _______ necessary to show that all 3 corresponding pairs of angles have equal measures. 

Are these two triangles similar?

• Yes, because all right triangles are similar.

• Yes, because they have one pair of corresponding angles whose measures are equal.

• No, because triangles with right angles cannot be similar to each other.

• Possibly, but we don’t have enough information to be certain.

Which statements about the triangles are true?  Select all that apply.

• △A∼△C

• △B∼△A

• △C∼△A

• △C∼△B

What information is needed to show △ABC∼△A′B′C′? If the measure of angle B' is 45 degrees, then the triangles ______ similar.

Sofia wants to determine the width of a lake that corresponds to segment DE in the diagram.  She marks segment BC because she knows that segment is parallel to segment DE.  She is able to determine that the length of segment BC is 12.612.6 meters. What is the length of segment DE to the nearest tenth of a meter? he length of segment DE is?

• 12.6

• 18.2

• 21.6

• 13.0

In the diagram shown, point M represents the location of a mirror between Gilbert and a flagpole.  The mirror is placed on the ground 88 feet in front of Gilbert so that he can see the top of the flagpole in the mirror. Based on the measurements in the diagram, what is the height, in feet, of the flagpole? The height of the flagpole is

• 5

• 12

• 15

• 24

What are the two lengths of sides JK and J′H′?

• 10.4

• 11.3

• 3.1

• 4.2