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Find the ratio of the areas of the two triangles in simplest form.
AΔ𝐴𝐡𝐢
=
AΞ”ABD
AΔ𝐴𝐡𝐢
=
AΞ”A𝐷𝐢
11-7: Ratios of Areas
Formulas so far…
β€’ 𝑨𝒔𝒒𝒖𝒂𝒓𝒆 = π’”πŸ
ο‚—
π‘¨π’•π’“π’‚π’‘π’†π’›π’π’Šπ’… =
ο‚—
π‘¨π’‘π’π’π’šπ’ˆπ’π’ = 𝒂 βˆ™ 𝒏 βˆ™ 𝒔
ο‚—
π‘ͺπ’Šπ’“π’„π’π’†π’”:
β—¦ 𝑨 = π…π’“πŸ
β—¦ π‘ͺ = πŸπ…π’“
β€’ π‘¨π’“π’†π’„π’•π’‚π’π’ˆπ’π’† = 𝒃 βˆ™ 𝒉
β€’ π‘¨π’‘π’‚π’“π’‚π’π’π’†π’π’π’ˆπ’“π’‚π’Ž = 𝒃 βˆ™ 𝒉
β€’ π‘¨π’•π’“π’Šπ’‚π’π’ˆπ’π’† =
𝟏
𝒃
𝟐
β€’ π‘¨π’“π’‰π’π’Žπ’ƒπ’–π’” =
𝟏
𝒅
𝟐 𝟏
βˆ™π’‰
βˆ™ π’…πŸ
𝟏
𝟐
π’ƒπŸ + π’ƒπŸ βˆ™ 𝒉
𝟏
𝟐
β—¦ 𝑨𝒔𝒆𝒄𝒕𝒐𝒓 =
𝜽
πŸ‘πŸ”πŸŽ
βˆ™ π…π’“πŸ
β—¦ π‘³π’†π’π’ˆπ’•π’‰ 𝒐𝒇 𝑨𝑩 =
𝜽
πŸ‘πŸ”πŸŽ
βˆ™ πŸπ…π’“
11-7 Objectives
β€’ Find the ratio of areas of two triangles.
β€’ Understand and apply the relationships
between scale factors, perimeters, and areas
of similar figures.
As we observed in the warm up…
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. What about similar triangles? …
Find the ratios of the areas of the similar
triangles and make a conjecture.
3
8
8
8
Is this true for any two similar shapes?
3
3
Yes. Yes it is.
:
If the scale factor of two similar figures is π‘Ž: 𝑏, then:
1. The ratio of the perimeters is π‘Ž: 𝑏.
2. The ratio of the areas is π‘Ž2 : 𝑏 2
(Recall, scale factor is the ratio of two corresponding side lengths of similar
polygons.)
Find the ratio of perimeters and areas
of the similar figures.
Find the ratio of perimeters and areas
of the similar figures.
Δ𝐴𝐷𝐢: π›₯𝐢𝐷𝐡
A pentagon with sides 3 π‘š, 4 π‘š, 4 π‘š, 6 π‘š, and
7 π‘š has area 48 π‘š2. Find the perimeter of a
similar pentagon whose area is 27 π‘š2.
p. 458 (bottom of page): #1-11 odd, 15, 17, 10, 16