Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3.

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Angle Relationships in TrianglesTriangles

Warm UpClassify each angle as acute, obtuse, or right.

1. 2.

3.

4. If the perimeter is 47, find x and the lengths of the three sides.

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Triangle Angles

Section 3.4

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Recall that a triangle ( ) is a polygon with three sides. Triangles can be classified in two ways: by their angle measures or by their side lengths.

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B

AC

AB, BC, and AC are the sides of ABC.

A, B, C are the triangle's vertices.

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Acute Triangle

Three acute angles

Triangle Classification By Angle Measures

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Equiangular Triangle

Three congruent acute angles


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Right Triangle

One right angle


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Obtuse Triangle

One obtuse angle


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Classify BDC by its angle measures.

Example 1A: Classifying Triangles by Angle Measures

Classify ABD by its angle measures.

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Classify FHG by its angle measures.

Example 1

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Equilateral Triangle

Three congruent sides

Triangle Classification By Side Lengths

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Isosceles Triangle

At least two congruent sides


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Scalene Triangle

No congruent sides


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Remember!When you look at a figure, you cannot assume segments are congruent based on appearance. They must be marked as congruent.

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Classify EHF by its side lengths.

Example 2A: Classifying Triangles by Side Lengths

Classify EHG by its side lengths.

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Classify ACD by its side lengths.

Example 2

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Find the side lengths of JKL.

Example 3: Using Triangle Classification

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Find the side lengths of equilateral FGH.

Example 3

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Lesson Review

Classify each triangle by its angles and sides.

1. MNQ

2. NQP

3. MNP

4. Find the side lengths of the triangle.

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Warm Up

1. Find the measure of exterior DBA of BCD, if mDBC = 30°, mC= 70°, and mD = 80°.

2. What is the complement of an angle with measure 17°?

3. How many lines can be drawn through N parallel to MP? Why?

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An auxiliary line is a line that is added to a figure to aid in a proof.

An auxiliary line used in the Triangle Sum

Theorem

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Example 1A: Application

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A corollary is a theorem whose proof follows directly from another theorem. Here are two corollaries to the Triangle Sum Theorem.

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The measure of one of the acute angles in a right triangle is 63.7°. What is the measure of the other acute angle?

Example 2a

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One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

Example 2: Finding Angle Measures in Right Triangles

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An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side.

Interior

Exterior

4 is an exterior angle.

3 is an interior angle.

The interior is the set of all points inside the figure. The exterior is the set of all points outside the figure.

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Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle.

Interior

Exterior

3 is an interior angle.

4 is an exterior angle.

The remote interior angles of 4 are 1 and 2.

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Find mB.

Example 3: Applying the Exterior Angle Theorem

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Find mACD.

Example 3

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Example 4

Find mP and mT.

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Find mK and mJ.

Example 4: Applying the Third Angles Theorem

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Lesson Review: Part I

1. The measure of one of the acute angles in a right triangle is 56 °. What is the measure of the other acute angle?

2. Find mABD. 3. Find mN and mP.

2 3

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Lesson Review: Part II

4. The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store?

Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3.

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Transcript of Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3.