Illustrative Mathematics - Geometry - Unit 3 - Lesson 15

In the right triangles shown, the measure of angle ABC is the same as the measure of angle EBD.  ​​​What is the length of side BE?

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In right triangle ABC, angle C is a right angle, AB=13, and BC=5. What is the length of AC?

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Select all of the right triangles.

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• {"blocks":[{"key":"767vk","text":"Triangle XYZ with XY=1, YZ=1, and XZ=2","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":9,"length":4,"style":"BOLD"},{"offset":9,"length":4,"style":"ITALIC"}],"entityRanges":[{"offset":19,"length":4,"key":0},{"offset":25,"length":4,"key":1},{"offset":35,"length":4,"key":2}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}},"1":{"type":"MATH","mutability":"MUTABLE","data":{}},"2":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"bc38i","text":"Triangle EFG with EF=8, FG=15, and EG=17","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":9,"length":4,"style":"BOLD"},{"offset":9,"length":4,"style":"ITALIC"}],"entityRanges":[{"offset":19,"length":4,"key":0},{"offset":25,"length":5,"key":1},{"offset":36,"length":5,"key":2}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}},"1":{"type":"MATH","mutability":"MUTABLE","data":{}},"2":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"8ctmv","text":"Triangle LMN with LM=7, MN=24, and AC=25","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":9,"length":4,"style":"BOLD"},{"offset":9,"length":4,"style":"ITALIC"}],"entityRanges":[{"offset":19,"length":4,"key":0},{"offset":25,"length":5,"key":1},{"offset":36,"length":5,"key":2}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}},"1":{"type":"MATH","mutability":"MUTABLE","data":{}},"2":{"type":"MATH","mutability":"MUTABLE","data":{}}}}
• {"blocks":[{"key":"6kmr9","text":"Triangle QRS with QR=4, RS=5, and QS=6","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":9,"length":4,"style":"BOLD"},{"offset":9,"length":4,"style":"ITALIC"}],"entityRanges":[{"offset":19,"length":4,"key":0},{"offset":25,"length":4,"key":1},{"offset":34,"length":5,"key":2}],"data":{}}],"entityMap":{"0":{"type":"MATH","mutability":"MUTABLE","data":{}},"1":{"type":"MATH","mutability":"MUTABLE","data":{}},"2":{"type":"MATH","mutability":"MUTABLE","data":{}}}}

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Andre says he can find the length of the third side of triangle ABC and it is 13 units. Mai disagrees and thinks that the side length is unknown. Who do you agree with? Show or explain your reasoning.

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In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also know AD=8 and DB=2. What is the value of h?

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