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Example 2 Proving that Two Triangles are Similar In the diagram, AABH ~ AKLH. Use properties of similar triangles to explain why these triangles are similar. A Solution B You can use the Vertical Angles Theorem to determine ZAHB = L_. Because they are right angles, ZABH = L By the can conclude that AABH K , you ΔKLH. ~

Example 2 Proving that Two Triangles are Similar In the diagram, AABH ~ AKLH. Use properties of similar triangles to explain why these triangles are similar. A Solution B You can use the Vertical Angles Theorem to determine ZAHB = L_. Because they are right angles, ZABH = L By the can conclude that AABH K , you ΔKLH. ~

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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This what I got so far <AHB = <KHL  because they are right angles <ABH =<KLH  

**Example 2: Proving that Two Triangles are Similar** In the diagram, △ABH ∼ △KLH. Use properties of similar triangles to explain why these triangles are similar. **Solution** You can use the Vertical Angles Theorem to determine ∠AHB ≅ ∠_____. Because they are right angles, ∠ABH ≅ ∠_____. By the __________, you can conclude that △ABH ∼ △KLH. **Diagram Explanation:** - The diagram shows two right triangles, △ABH and △KLH. - Triangle △ABH has a right angle at B, labeled as ∠ABH. - Triangle △KLH has a right angle at K, labeled as ∠KLH. - The triangles share a common angle, ∠AHB, which is vertically opposite to ∠KHL. The Vertical Angles Theorem can be applied here to show the equality of the respective angles, proving the triangles are similar by AA (Angle-Angle) similarity criterion.
Transcribed Image Text:**Example 2: Proving that Two Triangles are Similar** In the diagram, △ABH ∼ △KLH. Use properties of similar triangles to explain why these triangles are similar. **Solution** You can use the Vertical Angles Theorem to determine ∠AHB ≅ ∠_____. Because they are right angles, ∠ABH ≅ ∠_____. By the __________, you can conclude that △ABH ∼ △KLH. **Diagram Explanation:** - The diagram shows two right triangles, △ABH and △KLH. - Triangle △ABH has a right angle at B, labeled as ∠ABH. - Triangle △KLH has a right angle at K, labeled as ∠KLH. - The triangles share a common angle, ∠AHB, which is vertically opposite to ∠KHL. The Vertical Angles Theorem can be applied here to show the equality of the respective angles, proving the triangles are similar by AA (Angle-Angle) similarity criterion.
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