Take a closer look at the three similar triangles animated previously:

• First, labels are added to each vertex and the intersection of the altitude and the hypotenuse of the original triangle.
• Second, labels are added to the altitude and the two segments of the original hypotenuse.
• Third, the original right triangle is rotated and the similar triangles are recreated.

From these three similar triangles, several similarity statements can be written.

When writing a similarity statement, it is important to remember that the order of the vertices must be written so that the corresponding vertices are in the same order.

• The original right triangle is ΔABC. The angle at vertex A is the right angle.
• There is also another right angle at point M, the intersection of the altitude and hypotenuse of ΔABC.

Write two similarity statements for ΔABC: one for the smaller triangle created by the altitude, and one for the larger triangle created by the altitude.

Smaller triangle: ΔABC ~ Δ________

Larger triangle: ΔABC ~ Δ_________

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Check Your Answer

Smaller triangle: ΔABC ~ ΔMBA
Larger triangle: ΔABC ~ ΔMAC