Similar triangles
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Transcript of Similar triangles
Similar Triangles
The AAA Similarity Postulate
If three angles of one triangle are congruent to three angle of another triangle, then the two triangles are similar.
The AAA Similarity Postulate
If Then
The AA Similarity Theorem
If Then
Example 1
RI II NO, RI =8, RB=3x+4,ON=16, and OB=x+18
Find a. RB b. OB Ans. x=2 RB=10 OB=20
The SAS Similarity Theorem
If two sides of one triangle are proportional to the corresponding two sides of another triangle and their respective included angles are congruent, then the triangles are similar.
The SAS Similarity Theorem
If
Example 2
Are the two triangles similar? Justify your answer.
The SSS Similarity Theorem
If the sides of one triangle are proportional to the corresponding sides of a second triangle, then the triangles are similar.
Similar right triangles
The L-L Similarity Theorem If the legs of a right triangle are proportional to the corresponding legs of another right triangle, the right triangles are similar.
The L-L Similarity Theorem
If
Similar right triangles
The H-L Similarity Theorem If the hypotenuse and a leg of a right triangle are proportional to the corresponding hypotenuse and leg of another right triangle, then the right triangles are similar.
The H-L Similarity Theorem
If
Example 3
In the figure UA
Proportional Segments
The Proportional Segments Theorem
If a line intersects two sides of a triangle at distinct points and is parallel to the third side, the line divides the two sides in two proportional segments.
The Proportional Segments Theorem
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|| BC, then
Example 4
In AB||QR. If OA=5,
PA=2, and BR=10,
find PB.
Example 5
A flagpole 8m high casts a shadow of 12m, while a nearby building casts a shadow of 60m. How high is a building?
Proportional Segments
The Bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.
Proportional Segments
If with AD an angle bisector, then
Example 6Find the value of x.