SIMILAR TRIANGLES Identify similar triangles Use similar triangles
![SIMILAR TRIANGLES • Identify similar triangles • Use similar triangles to solve problems Eiffel SIMILAR TRIANGLES • Identify similar triangles • Use similar triangles to solve problems Eiffel](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-1.jpg)
![POSTULATE Angle-Angle (AA) Similarity If the two angles of one triangle are congruent to POSTULATE Angle-Angle (AA) Similarity If the two angles of one triangle are congruent to](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-2.jpg)
![THEOREM Side-Side (SSS) Similarity If the measures of the corresponding sides of two triangles THEOREM Side-Side (SSS) Similarity If the measures of the corresponding sides of two triangles](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-3.jpg)
![THEOREM Side-Angle-Side (SAS) Similarity If the measures of two sides of a triangle are THEOREM Side-Angle-Side (SAS) Similarity If the measures of two sides of a triangle are](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-4.jpg)
![Example 1 – Determine Whether Triangles are Similar In the figure, , BE = Example 1 – Determine Whether Triangles are Similar In the figure, , BE =](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-5.jpg)
![Example 1 – Determine Whether Triangles are Similar In the figure, , BE = Example 1 – Determine Whether Triangles are Similar In the figure, , BE =](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-6.jpg)
![Example 1 – Determine Whether Triangles are Similar In the figure, , BE = Example 1 – Determine Whether Triangles are Similar In the figure, , BE =](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-7.jpg)
![THEOREM Similarity of triangles is reflexive, symmetric, and transitive. Examples: Reflexive: ∆ABC ~ ∆ABC THEOREM Similarity of triangles is reflexive, symmetric, and transitive. Examples: Reflexive: ∆ABC ~ ∆ABC](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-8.jpg)
![Example 2 – Parts of Similar Triangles Algebra: Find AE and DE C A Example 2 – Parts of Similar Triangles Algebra: Find AE and DE C A](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-9.jpg)
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![SIMILAR TRIANGLES Identify similar triangles Use similar triangles to solve problems Eiffel SIMILAR TRIANGLES • Identify similar triangles • Use similar triangles to solve problems Eiffel](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-1.jpg)
SIMILAR TRIANGLES • Identify similar triangles • Use similar triangles to solve problems Eiffel Tower
![POSTULATE AngleAngle AA Similarity If the two angles of one triangle are congruent to POSTULATE Angle-Angle (AA) Similarity If the two angles of one triangle are congruent to](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-2.jpg)
POSTULATE Angle-Angle (AA) Similarity If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Example:
![THEOREM SideSide SSS Similarity If the measures of the corresponding sides of two triangles THEOREM Side-Side (SSS) Similarity If the measures of the corresponding sides of two triangles](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-3.jpg)
THEOREM Side-Side (SSS) Similarity If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar. Example: S Q a P ax b c bx R T cx U
![THEOREM SideAngleSide SAS Similarity If the measures of two sides of a triangle are THEOREM Side-Angle-Side (SAS) Similarity If the measures of two sides of a triangle are](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-4.jpg)
THEOREM 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. S Q Example: a P ax b bx R T U
![Example 1 Determine Whether Triangles are Similar In the figure BE Example 1 – Determine Whether Triangles are Similar In the figure, , BE =](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-5.jpg)
Example 1 – Determine Whether Triangles are Similar In the figure, , BE = 15, CF = 20, AE = 9, and DF = 12. Determine which triangles in the figure are similar. C B G A F E D
![Example 1 Determine Whether Triangles are Similar In the figure BE Example 1 – Determine Whether Triangles are Similar In the figure, , BE =](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-6.jpg)
Example 1 – Determine Whether Triangles are Similar In the figure, , BE = 15, CF = 20, AE = 9, and DF = 12. Determine which triangles in the figure are similar. C Solution: B Triangle FGE is an isosceles triangle, so G A F E D
![Example 1 Determine Whether Triangles are Similar In the figure BE Example 1 – Determine Whether Triangles are Similar In the figure, , BE =](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-7.jpg)
Example 1 – Determine Whether Triangles are Similar In the figure, , BE = 15, CF = 20, AE = 9, and DF = 12. Determine which triangles in the figure are similar. C If the measures of the corresponding sides that include the angles are proportional, then the triangles are similar. B G A By SAS similarity, ∆ABE ~ ∆DCF F E D
![THEOREM Similarity of triangles is reflexive symmetric and transitive Examples Reflexive ABC ABC THEOREM Similarity of triangles is reflexive, symmetric, and transitive. Examples: Reflexive: ∆ABC ~ ∆ABC](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-8.jpg)
THEOREM Similarity of triangles is reflexive, symmetric, and transitive. Examples: Reflexive: ∆ABC ~ ∆ABC Symmetric: If ∆ABC ~ ∆DEF, then ∆DEF ~ ∆ABC Transitive: If ∆ABC ~ ∆DEF and ∆DEF ~ ∆GHI, then ∆ABC ~ ∆GHI
![Example 2 Parts of Similar Triangles Algebra Find AE and DE C A Example 2 – Parts of Similar Triangles Algebra: Find AE and DE C A](https://slidetodoc.com/presentation_image_h/b96e215458a1cc9c2ebe8ac25dc880ec/image-9.jpg)
Example 2 – Parts of Similar Triangles Algebra: Find AE and DE C A X-1 2 B 5 E X+5 D
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