Geometry 2:Triangle Similarity REVIEWName:______
G-SRT.5. Learning Target: I can solve problems using similarity criteria for triangles. I can prove relationships in geometry figures using similarity criteria for triangles.
1. Jose wants to find the height of a building. Jose is standing 15 feet away from the tree. The tree is 12-feet tall. The tree is 26 feet away from the building.
(a) Draw a picture with the information given.
(b) How are the two triangles similar? ______
(b) What is the height of the building? (Round to the nearest foot.)
2.Karen wanted to measure the height of her school's flagpole. She placed a mirror on the ground 46 feet from the flagpole, and then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 13 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot. (Figures may not be drawn to scale)
3. Use the picture below to answer the following questions.
(a) Is there enough information to prove the two triangles are similar? Explain. ______
______
(b) If so, find the value of x. If not, what additional information would be needed?
4. Given the two similar triangles shown below,
(a) What similarity method makes it possible to find the value of x? ______
(b) Find the value of x.
G-GPE.6. Learning Target: I can find the point on a directed line segment between two given points that partitions the segment in a given ratio.
5. Line segment AB in the coordinate plane has endpoints with coordinates A ( and Graph and find the locations of point P so that P divides into two parts with lengths in a ratio of 1:4.
NOTE: There are TWO possible answers. You must find both for full credit.
Show all of your work.
G-SRT.1. Learning Target: I can verify the following statements by making multiple examples: a dilation of a line is parallel to the original line if the center of dilation is not on the line; a dilation of a line segment changes the length by a ratio given by the scale factor.
6.Graph with and on the coordinate plane below.
(a)Graph the dilation ofusing the origin as the center and a scale factor of . Label the dilation .
(b)Are the two segments parallel, perpendicular, coinciding, or none of the above? ______
(c)Find the length of the and .
(d)Find the value of the ratio of the length of the dilated segment to the length of the original segment.
7. Given the segment shown below. If it is dilated about Point U, complete the following statements:
(a). The slopes of the segments will be ______, so the segments will be
(reciprocal, same, different)
______
(parallel, perpendicular, coinciding – choose one)
(b) The segments will be ______
(congruent, similar, neither – choose one)
because ______
______