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Congruent Polygon -

Similar Polygon -

Ratio

Proportion

11.1 Similar Polygons

Hexagon ABCDEF is similar to Hexagon PQRSTU

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Transformations

rigid -

non-rigid -

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2 4 6

-2

-4

-6

2

4

6

-6 -4 -2

y

x

C-92 Dilation Similarity ConjectureIf one polygon is the image of another polygon under a dilation then the polygons are similar.

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11.2 Similar Triangles

Shortcuts:

Congruences

Similarity

What needs to be true for triangles to be similar?

Look for counterexamples

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Two congruent angles

C-93 AA Similarity ConjectureIf two angles of one triangle are congruent to two angles of another triangle then the triangles are similar.

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Two sides in proportion

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Three sides in proportion

C-94 SSS Similarity Conjecture If the three sides of one triangle are proportional to the three sides of another triangle, then the two triangles are similar.

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Two sides in proportion and a congruent angle

included angle

adjacent angle

C-95 SAS Similarity ConjectureIf two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent; triangles are similar.

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* Go through estimating the height of the ceiling using a mirror

Lynda is standing 4 ft behind a fence 6.5ft. tall. When she looks over the fence, she can just see the top edge of a building. She knows that the building is 32.5ft behind the fence. Her eyes are 5 ft from the ground. How tall is the building?

You need to add 5 supports under a ramp, in addition to a 3.6m one at the end, so that they are all equally spaced. How long should each support be?

Driving through the mountains, Jon has to go up and over a high mountain pass. The road has a constant incline for 7.75 miles to the top of the pass. Jon notices from a road sign that in the first mile he climbs 840 feet. What is the height of the mountain pass?

March 18, 2015

2 4 6

-2

-4

-6

2

4

6

-6 -4 -2

y

x

March 18, 2015

2 4 6

-2

-4

-6

2

4

6

-6 -4 -2

y

x