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Lesson 62
Course 2-Student Notes
Objective: TSW classify a triangle by its angles. TSW classify a triangle by its sides.
Recall from Lesson 7 that we classify angles as acute angles, right angles, and obtuse angles.
We use these same words to describe triangles that contain these angles. If every angle of a triangle measures
less than 90°, then the triangle is an _______________ triangle. If the triangle contains a 90° angle, then the
triangle is a _______________ triangle. An ___________________ triangle contains one obtuse angles that
measures more than 90°.
Question: What is the total angle measure of a triangle?
Question: Can a triangle have two obtuse angles? Why or Why not?
When describing triangles, we can refer to the sides and angles as "opposite" each other. For example, we
might say, "The side opposite the right angle is the longest side of the right triangle." The side opposite an
̅̅̅̅ is the side opposite ∠𝐶 and ∠𝐶 is the angle
angle is the side the angle opens toward. In this right triangle, 𝐴𝐵
opposite side AB.
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Example 1.
Name the sides of this triangle in order from shortest to longest.
If two angles of a triangle are the same measure, then their opposite sides are the same length.
Example 2.
Which sides of this triangle are the same length?
If all three angles of a triangle are the same measure, then all three sides are the same length.
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Example 3.
The triangle in Example 3 is a regular triangle. We usually call a regular triangle an
_______________________ triangle. As shown below, the three angles of an equilateral triangle each
measure 60°, and the three sides are the same length. The tick marks on the sides indicate sides of equal
length, while tick marks on the arcs indicate angles of equal measure.
If a triangle has at least two sides of the same length (and thus two angles of the same measure), then the
triangle is called an ________________________ triangle. The triangle in example 2 is an isosceles triangle, as
are each of these triangles:
If the three sides of a triangle are all different lengths (and thus the angles are all different measures), then
the triangle is called a __________________ triangle.
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Example 4
The perimeter of an equilateral triangle is 2 feet. How many inches long is each side.
Example 5
Draw an isosceles right triangle.
Question: What is the measure of each of the angles opposite the sides you drew?
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You Try!!