Warm Up Classify each angle as acute, obtuse, or right. 1. 2. 3. 1. 2. 3. 4. If the perimeter is 47, find x and the lengths of the three sides. acute right obtuse x = 5; 8; 16; 23

Section 4-1: Classifying Triangles

What we’re going to learn… How do classify triangles based on the measures of their angles and the length of their sides. How to use triangle classifications to find measures of angles and lengths of sides.

Aligning SC Standards G-1.8: Connect geometry with other branch of mathematics G-3.1: Carry out a procedure to compute the perimeter of a triangle. G-3.4: Apply properties of isosceles and equilateral triangles to solve problems.

What do you know? (Activate Prior Knowledge) about triangles? What do you THINK you know about triangles? Students get in tribes and discuss collaboratively what they know about triangles and what they kind of know about triangles. Students will quickly brainstorm on their own first and then create a list for the group as a whole. (3 min.) As a whole group (class), we will discuss and fill in this chart on the smart board. Teacher will walk the room and get a student to fill in the chart.

What you WILL know? (Lesson Preview) * acute triangle equiangular triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle Pass out graphic organizer for notes

2 Ways to Classify Triangles By Angles By Sides

C A B AB, BC, and AC are the sides of ABC. A, B, C are the triangle's vertices.

Three congruent acute angles Triangle Classification By Angle Measures Equiangular Triangle Three congruent acute angles

Classifying Triangles by Angles Equiangular All the angles are congruent

Acute Triangle Three acute angles Triangle Classification By Angle Measures Acute Triangle Three acute angles

Classifying Triangles by Angles Acute All the angles are acute

Right Triangle One right angle Triangle Classification By Angle Measures Right Triangle One right angle

Classifying Triangles by Angles Right One angle is right or 90°

Obtuse Triangle One obtuse angle Triangle Classification By Angle Measures Obtuse Triangle One obtuse angle

Classifying Triangles by Angles Obtuse One angle is obtuse

Examples – Classifying Triangles by Angles 33° 57° Classify the triangle to the left. Right Triangle

Examples – Classifying Triangles by Angles Classify the triangle to the left. 60 ° 60° 60° Equiangular

Examples – Classifying Triangles by Angles Classify the triangle to the left. Obtuse Triangle

Examples – Classifying Triangles by Angles Classify the triangle to the left. 83.1° 44.7° 52.2° Acute Triangle

You Try – Classifying Triangles by Angles 60 ° 60° Classify the triangle to the left. Equiangular

You Try – Classifying Triangles by Angles 45° Classify the triangle to the left. Right Triangle

You Try – Classifying Triangles by Angles Classify the triangle to the left. 88° 45° 47° Acute Triangle

You Try – Classifying Triangles by Angles Classify the triangle to the left. 110° Obtuse Triangle

Example 1A: Classifying Triangles by Angle Measures Classify BDC by its angle measures. B is an obtuse angle. B is an obtuse angle. So BDC is an obtuse triangle.

Example 1B: Classifying Triangles by Angle Measures Classify ABD by its angle measures. ABD and CBD form a linear pair, so they are supplementary. Therefore mABD + mCBD = 180°. By substitution, mABD + 100° = 180°. So mABD = 80°. ABD is an acute triangle by definition.

Check It Out! Example 1 Classify FHG by its angle measures. EHG is a right angle. Therefore mEHF +mFHG = 90°. By substitution, 30°+ mFHG = 90°. So mFHG = 60°. FHG is an equiangular triangle by definition.

Equilateral Triangle Three congruent sides Triangle Classification By Side Lengths Equilateral Triangle Three congruent sides

Classifying Triangles by Sides Equilateral All sides are congruent

At least two congruent sides Triangle Classification By Side Lengths Isosceles Triangle At least two congruent sides

Classifying Triangles by Sides Isosceles 2 sides are congruent

Scalene Triangle No congruent sides Triangle Classification By Side Lengths Scalene Triangle No congruent sides

Classifying Triangles by Sides Scalene NO sides are congruent

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

Examples - Classifying Triangles by Sides Classify the triangle to the right. ISOSCELES

Examples - Classifying Triangles by Sides Classify the triangle to the right. SCALENE

Examples - Classifying Triangles by Sides Classify the triangle to the right. EQUILATERAL

You Try - Classifying Triangles by Sides Classify the triangle to the right. SCALENE

You Try - Classifying Triangles by Sides Classify the triangle to the right. EQUILATERAL

You Try - Classifying Triangles by Sides Classify the triangle to the right. ISOSCELES

Example 2A: Classifying Triangles by Side Lengths Classify EHF by its side lengths. From the figure, . So HF = 10, and EHF is isosceles.

Example 2B: Classifying Triangles by Side Lengths Classify EHG by its side lengths. By the Segment Addition Postulate, EG = EF + FG = 10 + 4 = 14. Since no sides are congruent, EHG is scalene.

Classify ACD by its side lengths. Check It Out! Example 2 Classify ACD by its side lengths. From the figure, So AC = 15, and ACD is isosceles.

Examples- Classifying Triangles Both Ways Classify the triangle to the right. OBTUSE SCALENE 30° 33° 117°

Examples- Classifying Triangles Both Ways Classify the triangle to the right. 48.5° 83° Acute IsoscELES

Examples- Classifying Triangles Both Ways Classify the triangle to the right. 60° Acute Equilateral 60° equiangular Equilateral 60°

You Try - Classifying Triangles Both Ways Classify the triangle to the right. RIGHT SCALENE 57° 90° 33°

You Try - Classifying Triangles Both Ways Classify the triangle to the right. 45° RIGHT ISOSCELES 45°

You Try- Classifying Triangles Both Ways Classify the triangle to the right. Acute SCALENE 61° 41° 78°

Example 3: Using Triangle Classification Find the side lengths of JKL. Step 1 Find the value of x. Given. JK = KL Def. of  segs. Substitute (4x – 10.7) for JK and (2x + 6.3) for KL. 4x – 10.7 = 2x + 6.3 Add 10.7 and subtract 2x from both sides. 2x = 17.0 x = 8.5 Divide both sides by 2.

Example 3 Continued Find the side lengths of JKL. Step 2 Substitute 8.5 into the expressions to find the side lengths. JK = 4x – 10.7 = 4(8.5) – 10.7 = 23.3 KL = 2x + 6.3 = 2(8.5) + 6.3 = 23.3 JL = 5x + 2 = 5(8.5) + 2 = 44.5

Check It Out! Example 3 Find the side lengths of equilateral FGH. Step 1 Find the value of y. Given. FG = GH = FH Def. of  segs. Substitute (3y – 4) for FG and (2y + 3) for GH. 3y – 4 = 2y + 3 Add 4 and subtract 2y from both sides. y = 7

Check It Out! Example 3 Continued Find the side lengths of equilateral FGH. Step 2 Substitute 7 into the expressions to find the side lengths. FG = 3y – 4 = 3(7) – 4 = 17 GH = 2y + 3 = 2(7) + 3 = 17 FH = 5y – 18 = 5(7) – 18 = 17

Example 4: Application A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam? The amount of steel needed to make one triangle is equal to the perimeter P of the equilateral triangle. P = 3(18) P = 54 ft

Example 4: Application Continued A steel mill produces roof supports by welding pieces of steel beams into equilateral triangles. Each side of the triangle is 18 feet long. How many triangles can be formed from 420 feet of steel beam? To find the number of triangles that can be made from 420 feet of steel beam, divide 420 by the amount of steel needed for one triangle. 420  54 = 7 triangles 7 9 There is not enough steel to complete an eighth triangle. So the steel mill can make 7 triangles from a 420 ft. piece of steel beam.

Check It Out! Example 4a Each measure is the side length of an equilateral triangle. Determine how many 7 in. triangles can be formed from a 100 in. piece of steel. The amount of steel needed to make one triangle is equal to the perimeter P of the equilateral triangle. P = 3(7) P = 21 in.

Check It Out! Example 4a Continued Each measure is the side length of an equilateral triangle. Determine how many 7 in. triangles can be formed from a 100 in. piece of steel. To find the number of triangles that can be made from 100 inches of steel, divide 100 by the amount of steel needed for one triangle. 100  7 = 14 triangles 2 7 There is not enough steel to complete a fifteenth triangle. So the manufacturer can make 14 triangles from a 100 in. piece of steel.

Check It Out! Example 4b Each measure is the side length of an equilateral triangle. Determine how many 10 in. triangles can be formed from a 100 in. piece of steel. The amount of steel needed to make one triangle is equal to the perimeter P of the equilateral triangle. P = 3(10) P = 30 in.

Check It Out! Example 4b Continued Each measure is the side length of an equilateral triangle. Determine how many 10 in. triangles can be formed from a 100 in. piece of steel. To find the number of triangles that can be made from 100 inches of steel, divide 100 by the amount of steel needed for one triangle. 100  10 = 10 triangles The manufacturer can make 10 triangles from a 100 in. piece of steel.

Homework (Choose 1 of the 3 options) Make a set of flash cards. One card for each of the 7 triangles. Put an image and name of each triangle on one side and a description on the back. List 7 real-world examples of where the 7 types of triangles can be seen. For example: Doritos® as equilateral triangles. (You cannot use mine ) Create a checklist of steps or things to check for when classifying triangles. For example: Step 1 – Examine the angle measures, etc.

Exit Slip In your brain, answer the following questions: What did you learn today? Which of the 7 triangles is your favorite and why?