Lesson 6-3 Similar Triangles. Ohio Content Standards:

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Presentation transcript:

Lesson 6-3 Similar Triangles

Ohio Content Standards:

Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two- dimensional figures and three- dimensional objects.

Ohio Content Standards: Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures).

Ohio Content Standards: Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.

Ohio Content Standards: Apply proportional reasoning to solve problems involving indirect measurements or rates.

Postulate 6.1 Angle-Angle (AA) Similarity

If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Theorem 6.1 Side-Side-Side (SSS) Similarity

If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar.

Theorem 6.2 Side-Angle-Side (SAS) Similarity

If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.

B C D E A

U S R T Q 10 2x + 10 x + 3 4

Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 p.m. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower ’ s shadow and it was 242 feet at that time. What is the height of the Sears Tower?

Assignment: Pgs evens, odds