Similarity In A Right Triangle When An Altitude Is Drawn From The Hypotenuse To The Right Angle.

So far, we know how to solve similarity in triangles, but how about having a right triangle with the height from the hypotenuse? Can you see the embedded triangles in the figure? May you determine which sides are corresponding for them to setup proportions? Do you know why they are similar?

In the process of solving these examples, you will explore them by separately drawing the embedded triangles and then relating the corresponding sides to build the proportions that will enable you to find the unknown segment lengths. If you try the suggested problems; you will be able to solve them with your stylus and taking advantage of the marker tools menu. It is a very visual approach, You will like it!

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Lesson's Glossary

Angle-angle-angle (AAA) similarity
The angle-angle-angle (AAA) similarity test states that given two triangles that have corresponding angles that are congruent, then the triangles are similar. As we know the sum of the interior angles in a triangle is 180°, so if two corresponding are congruent, then the other ones should be as well.

Proportion
A statement that two ratios are equal.

Proportional
One of four numbers that form a true proportion.

Pythagorean theorem  a2 + b2 = c2.
The Pythagorean theorem states that if you have a right triangle, then the square built on the hypotenuse is equal to the sum of the squares built on the other two sides.


Ratio
A quotient of 2 numbers.

Right triangle
A triangle that has a 90 degree angle.


Side-angle-side (SAS) similarity
The side-angle-side (SAS) similarity test states that given two triangles that have two pairs of sides that are proportional and the included angles are congruent, then the triangles should be similar.

Side-side-side (SSS) similarity
The side-side-side (SSS) similarity test states that for two triangles to be similar; all corresponding sides should be proportional.

Similar
Two polygons are similar polygons if corresponding angles have the same measure and corresponding sides are in proportion.

Similar triangles
Similar triangles are triangles which have the same shape but probably different size. Corresponding angles need to be congruent, and corresponding sides are in proportion.

Triangle
A polygon with three sides.

 

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