. . . to use proportions to solve problems involving similar figures. Today’s Lesson: What: similar Figures Why: . . . to use proportions to solve problems involving similar figures.

What are similar figures ? Similar figure – figures that are the same shape, but a different _________. size SAME shape! DIFFERENT size! CONGRUENT angles! PROPORTIONAL sides!

Identifying corresponding sides . . . WZ WX XY YZ B D

Identifying corresponding sides . . . DF EF D E 35°

Notice that this is BIG on top and SMALL on bottom! Solve for a missing side-length: Trapezoid ABCD is similar to trapezoid WXYZ (one is a reflection/dilation of the other). Solve for the missing side-length. Write corresponding sides as a ratio on each side of the proportion . . . 𝟓 𝟐 = 𝟏𝟐.𝟓 𝐱 5x = 25 Notice that this is BIG on top and SMALL on bottom! 5 5 x = 5 cm

Solve for a missing side-length: Triangle ABC is similar to triangle DEF (one is a rotation/dilation of the other). Solve for the missing side-length. Solve for a missing side-length: x = 5 cm

Solve for a missing side-length: 2 Similar Triangles – What is the value of “x”? x = 19.2 in.

Solve for a missing side-length: A 9.5 ft. tall tree casts a shadow 15 ft. in length. A nearby building casts a shadow that is 45 ft. in length. How tall is the building? x = 28.5 ft.

Identifying similar figures . . . Which triangle below is similar to triangle DEF (circle your choice) ? Write given sides on original triangle as a ratio. Then, write the other triangle’s corresponding sides as ratios. Cross-multiply to find out which ratio is equal to original! ORIGINAL triangle!

END OF LESSON