SWBAT… classify triangles in the coordinate plane Thurs, 3/6 SWBAT… classify triangles in the coordinate plane Agenda Warm-up: (10 min) Classifying triangles (40 min) Warm-Up: Write your HW in your planners Homework: Isosceles and Equilateral Triangles #1 – #8 #9: Is the triangle scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0) 1

Unit 5: Classifying Triangles

Classification means put things into a group according to how they are alike.

We will break this group of animals into smaller groups.

Can't Fly Can Fly The same animals can be put into different groups depending on what we look at when we classify them. Extinct Still Living

Today you will learn how triangles can be classified in two different ways...

Think of all the different kinds of triangles you know. Did you come up with all of these? Acute Obtuse Right Scalene Isosceles Equilateral

Triangle The three endpoints are called vertices. A polygon with 3 angles and 3 straight sides. The three endpoints are called vertices.

Classifying by side lengths Isosceles at least two Scalene none Equilateral all 3

Scalene Triangle All sides are different lengths.

Isosceles Triangle Two out of the three sides are equal lengths.

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Ex. If AC = BC, name two congruent angles.

Equilateral Triangle All sides have the same length

Properties of Equilateral Triangles A triangle is equilateral if and only if it is has three congruent angles (all the measures would then be 600.)

d = 5 Divide each side by 3. KL = 7, LM = 7, KM = 7 Ex. KLM is an equilateral triangle with KL = d + 2, LM = 12 – d, KM = 4d – 13. Find d and the measure of each side. 4d – 13 = d + 2 Substitution 3d – 13 = 2 Subtract d from each side. 3d = 15 Add 13 to each side. d = 5 Divide each side by 3. KL = 7, LM = 7, KM = 7 Example 1-3a

Classify this triangle by its sides. ISOSCELES

Classify this triangle by its sides. SCALENE

Classify this triangle by its sides. EQUILATERAL

Classify the following triangles by their sides. Use these signals: Scalene Isosceles Equilateral

Classify by sides. Give the best name. Scalene Isosceles Equilateral

Classify by sides. Give the best name. Scalene Isosceles Equilateral

Classify by sides. Give the best name. Scalene Isosceles Equilateral

What formula do you use to determine if a triangle is scalene, isosceles, or equilateral? Answer: The terms scalene, isosceles, and equilateral have to do with side lengths of a triangle so you use the Distance Formula.

Classifying by angle measures Acute acute right Right Obtuse obtuse

Acute Triangle All three angles are less than 900. 800 400 600

Obtuse Triangle One of the three angles is more than 900 200 300 1300

Right Triangle One of the three angles is exactly 900

Classify the following triangles by their sides. Use these signals: Acute Obtuse Right

Classify by angles. Acute Obtuse Right

Classify by angles. 1000 Acute Obtuse Right

Classify by angles. 850 450 500 Acute Obtuse Right

A B C D E Now you should be able to classify any triangle by both its side lengths and its angles.

Classify the triangles by sides lengths and angles a) b) c) 7 40° 15° 25 24 70° 70° 120° 45° Solutions: Scalene, Right Isosceles, Acute Scalene, Obtuse

Example 1 Classify a triangle in a coordinate plane Determine whether PQO with vertices at P(-1, 2), Q(6, 3), O(0, 0), is scalene, isosceles, or equilateral. Explain. SOLUTION Use the distance formula to find the side lengths. OP = y 2 – 1 ( ) x + = 2 – ( ) (– 1 ) + 5 2.2 OQ = y 2 – 1 ( ) x + 2 = – ( ) 6 + 3 45 6.7 PQ = y 2 – 1 ( ) x + 3 – 2 ( ) 6 + = (– 1 ) 50 7.1

PQO is a scalene triangle since none of the sides are congruent. EXAMPLE Classify a triangle in a coordinate plane (continued) PQO is a scalene triangle since none of the sides are congruent. Explanation

HW: Isosceles and Equilateral Triangles #1 – #8 #9: Is ABC scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0)

Using the ruler, draw triangles with the following side measures: a.) 3cm, 4cm, 6cm b.) 2cm, 2cm, 6cm

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Ex: Can these be the measures of a triangle? a.) 3cm, 4cm, 6cm b.) 2cm, 2cm, 6cm

Example: Find value of x and missing side measurement

Ex. Find the measure of each side of equilateral  RST with RS = 2x + 2, ST = 3x, and TR = 5x – 4. 5x – 4 = 2x + 2 x = 2 RS = 6 ST = 6 TR = 6

Ex. Find the measure of each side of isosceles  ABC with AB = BC if AB = 4y, BC = 3y + 2, and AC = 3y. 3y + 2 = 4y y = 2 AB = 8 BC = 8 AC = 6

Ex. Find x of isosceles right  WZY if angle YWZ = 900, WZ = WY, and WYZ = 3x. 3x + 3x + 90 = 180 x = 15

Example: Find missing angle measurements

c. equilateral triangles Ex: Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, BCE, BDE, CDE, ACD, ABD c. equilateral triangles Answer: None! Example 1-2c

Exit Slip Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain. Answer: AB = 5 BC = 5 CA = 7.1 Since AB = Triangle ABC is isosceles since two of the sides are congruent.

#1 – #4: Find x: 4x – 4 3x + 8 600 1.) 2.) 3.) 4.) 5.) Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain. 6x0 2x0 400 (4x – 5)0

SWBAT… classify triangles in the coordinate plane Mon, 3/10 SWBAT… classify triangles in the coordinate plane Agenda Warm-up: (10 min) 4 Examples (25 min) Review HW (10 min) Warm-Up: Find the missing angles: HW: Re-do 5 problems - Worksheet <1 = 630 <2 = 630 <3 = 380 48

Warm-Up: What is Congruent? AB  ________ BD  _______  _______  _______ CBE  ________  BCE BDE  ________ ABC  ________

Example: Find missing angle measurements

Name the missing coordinates of isosceles right triangle ABC. Answer: C(0, 0); A(0, d)

Name the missing coordinates of isosceles right triangle SRQ. Answer: Q(0, 0); S(c, c)

Find the missing angles.

Warm-Up: Find the missing angles.

Warm-Up Find the missing angles.

Warm-Up: Find the missing angles.

What do you know about the Pythagorean Theorem? Homework: Collected. What do you know about the Pythagorean Theorem? Formula? When and why it’s used? Solve for x: 10 x 3 6 4 x