Using the Pythagorean Theorem and Similarity

​Using the Pythagorean Theorem and Similarity

Let’s explore right triangles with altitudes drawn to the hypotenuse.

I can find similar triangles formed by the altitude to the hypotenuse in a right triangle.

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​Learning Target

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​altitude

An altitude in a triangle is a line segment from a vertex to the opposite side that is perpendicular to that side. Triangles formed by drawing the altitude to the hypotenuse must be similar

Open Ended

Is triangle ADC similar to triangle CDB? Explain or show your reasoning.

​Yes, because both triangles have angles that measure 37, 53, and 90 degrees. Corresponding angles from the similarity statements are congruent.

Open Ended

Write 3 similarity statements. showing the three triangles are similar.

Open Ended

Determine the scale factor for each pair of triangles.

Open Ended

Determine the lengths of sides HG, GF, and HF.

Open Ended

The diagram shows 3 similar triangles.

Find the value of AD.

I can find similar triangles formed by the altitude to the hypotenuse in a right triangle.

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​Learning Target

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Open Ended

Find the lengths of segments AB and BD. Then check your answers using a different method.