5-1 Classifying Triangles Geometry

Today we will be learning how to classify triangles according to length of sides and measurement of the angles.

First we will learn to classify by the ANGLES

Right triangles have ONE right angle

Acute Triangles have three acute angles Smaller than 90o Smaller than 90o Smaller than 90o

Obtuse Triangles have ONE obtuse angle

We will now learn to classify triangles by their sides.

Equilateral Triangles have 3 equal sides If you collapsed all of the sides they would form a line.

Isosceles Triangles have 2 equal sides.

Scalene Triangles have NO equal sides.

Classifying Triangles by Their Sides EQUILATERAL – 3 congruent sides ISOSCELES – at least two sides congruent SCALENE – no sides congruent EQUILATERAL ISOSCELES SCALENE

Classifying Triangles by Their Angles EQUIANGULAR – all angles are congruent ACUTE – all angles are acute RIGHT – one right angle OBTUSE – one obtuse angle ACUTE EQUIANGULAR RIGHT OBTUSE

Can You Classify the Different Triangles in the Picture Below? Classify the following triangles: AED, ABC, ACD, ACE Triangle AED = Equilateral, Equiangular Triangle ABC = Equilateral, Equiangular Triangle ACD = Isosceles, Obtuse Triangle ACE = Scalene, Right

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You have now learned that triangles can be classified by either their sides or their angles.

5-2 Angles of a Triangle

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Write and solve an equation to find the value of x. EXAMPLE 3 Find an angle measure Find m∠ JKM. SOLUTION STEP 1 Write and solve an equation to find the value of x. (2x – 5)° = 70° + x° Apply the Exterior Angle Theorem. x = 75 Solve for x. STEP 2 Substitute 75 for x in 2x – 5 to find m∠ JKM. 2x – 5 = 2 75 – 5 = 145 The measure of ∠ JKM is 145°. ANSWER

GUIDED PRACTICE for Examples 3 and 4 Find the measure of 1 in the diagram shown. The measure of ∠ 1 in the diagram is 65°. ANSWER

GUIDED PRACTICE for Examples 3 and 4 x 2x 3x Find the measure of each interior angle of ABC, where m A = x , m B = 2x° , and m C = 3x°. ° SOLUTION A + B + C = 180° x + 2x + 3x = 180° 6x = 180° x = 30° B = 2x = 2(30) = 60° C = 3x = 3(30) = 90°

GUIDED PRACTICE for Examples 3 and 4 Find the measures of the acute angles of the right triangle in the diagram shown. 26° and 64° ANSWER