+

Ratios of Areas

11-7 PG 456

Pg 465

HW: pg 458 – 4591 - 21

+Comparing Areas of Triangles

(Purple Text)

Comparing Areas of Triangles

1) If two triangles have equal heights, then the ratio of their areas equals the ratio of their bases.

2) If two triangles have equal bases, then the ratio of their areas equals the ratio of their heights.

3) If two triangles are similar then the ratio of their areas equals the square of their scale factor.

+Example 1) Look in your book, copy down if needed.

A) with equal height

B) With equal bases C) scale factor

+2 examples on the side board& more

Directions: Find the ratio of the areas in each figure below.

3) The ratio of the corresponding heights of two similar triangles is 3:5. What is the ratio of the corresponding sides?

What is the ratio of the perimeters?

What is the ratio of the areas?

+True of False 4) If two quadrilaterals are similar, then their areas

must be in the same ratio as the square of the ratio of their perimeters.

5) If the ratio of the areas of two equilateral triangles is 1:3, then the ratio of the perimeters is 1: (3)^.5 or the square root of 3.

6) If the ratio of the perimeters of two rectangles is 4:7, then the ratio of their areas must be 16:49.

7) If the ratio of the areas of two squares is 3:2 then the ratio of their sides must be (3)^.5 : (2)^.5, square root of both numbers.

+Classroom Exercises pg 458, 1 - 15

+Answers:

1) 9/5 ; 2) 9/16 ; 3) 5/6

4) 1:3; 1:9 ; 5) 1:5 ; 1:25 6) 3:4 ; 9:16

7) 2:3 ; 4:9 8) 4:5 ; 16:25 9) 3:5 ; 9:25

10) 4:7 ; 4:7 11) 6:5 ; 6:5

12) A) yes B) 3:4 ; 9:16

13) a) No B) tri ABC ~ tri ABC C) 4:25D) 4:21

14) 8:5 ; 8:15 15) 7:4 ; 49:16