A triangle has an angle measuring 90^∘, an angle measuring 20^∘, and a side that is 6 units long

step 1 In problem two, we are told that a triangle has an angle measuring 90 degrees and 20 degrees, an

A triangle has an angle measuring 90^∘, an angle measuring...

A triangle has an angle measuring $90^{\circ}$, an angle measuring $20^{\circ}$, and a side that is 6 units long. The 6-unit side is in between the $90^{\circ}$ and $20^{\circ}$ angles. a. Sketch this triangle and label your sketch with the given measures. b. How many unique triangles can you draw like this?

A triangle has an angle measuring $90^{\circ}$, an angle measuring $20^{\circ}$, and a side that is 6 units long. The 6-unit side is in between the $90^{\circ}$ and $20^{\circ}$ angles.
a. Sketch this triangle and label your sketch with the given measures.
b. How many unique triangles can you draw like this?

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Key Concepts

Triangle Angle Sum Property

This property states that the sum of the interior angles of any triangle is 180°. Knowing two angles allows you to immediately find the third, which is crucial in determining the triangle’s complete set of angles and ensuring the triangle is constructed correctly.

ASA Congruence Criterion

The Angle-Side-Angle (ASA) congruence criterion establishes that if two angles and the included side of one triangle are equal to the corresponding parts of another triangle, then the two triangles are congruent. This concept leads to the conclusion that only one unique triangle can be constructed when given an angle-side-angle configuration.

Right Triangle Properties

A right triangle is defined by having one 90° angle, which gives the triangle distinct characteristics such as the Pythagorean theorem and specific trigonometric ratios. These properties simplify many calculations and provide a firm structure for the triangle, ensuring a unique solution when combined with additional angle and side information.

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