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Contents Lesson 4-1Classifying Triangles Lesson 4-2Angles of Triangles Lesson 4-3Congruent Triangles Lesson 4-4Proving Congruence–SSS, SAS Lesson 4-5Proving Congruence–ASA, AAS Lesson 4-6Isosceles Triangles Lesson 4-7Triangles and Coordinate Proof

Lesson 1 Contents Example 1Classify Triangles by Angles Example 2Classify Triangles by Sides Example 3Find Missing Values Example 4Use the Distance Formula OBJECTIVE: To identify and classify triangles by angles (2.9.8D) (M8.C.1.1)

Example 1-1a ARCHITECTURE The triangular truss below is modeled for steel construction. Classify  JMN,  JKO, and  OLN as acute, equiangular, obtuse, or right.

Example 1-1a Answer:  JMN has one angle with measure greater than 90, so it is an obtuse triangle.  JKO has one angle with measure equal to 90, so it is a right triangle.  OLN is an acute triangle with all angles congruent, so it is an equiangular triangle.

Example 1-1b ARCHITECTURE The frame of this window design is made up of many triangles. Classify  ABC,  ACD, and  ADE as acute, equiangular, obtuse, or right. Answer:  ABC is acute.  ACD is obtuse.  ADE is right.

Example 1-2a Answer:  UTX and  UVX are isosceles. Identify the isosceles triangles in the figure if Isosceles triangles have at least two sides congruent.

Example 1-2b Identify the scalene triangles in the figure if Answer:  VYX,  ZTX,  VZU,  YTU,  VWX,  ZUX, and  YXU are scalene. Scalene triangles have no congruent sides.

Example 1-2c Identify the indicated triangles in the figure. a. isosceles triangles b. scalene triangles Answer:  ABC,  EBC,  DEB,  DCE,  ADC,  ABD Answer:  ADE,  ABE

Example 1-3a ALGEBRA Find d and the measure of each side of equilateral triangle KLM if and Since  KLM is equilateral, each side has the same length. So Substitution Subtract d from each side. Add 13 to each side. Divide each side by 3.

Example 1-3b Next, substitute to find the length of each side. Answer: For  KLM, and the measure of each side is 7.

Example 1-3c Answer: ALGEBRA Find d and the measure of each side of equilateral triangle if and

Example 1-4a COORDINATE GEOMETRY Find the measures of the sides of  RST. Classify the triangle by sides.

Example 1-4b Answer: ; since all 3 sides have different lengths,  RST is scalene. Use the distance formula to find the lengths of each side.

Example 1-4c Find the measures of the sides of  ABC. Classify the triangle by sides. Answer: ; since all 3 sides have different lengths,  ABC is scalene.

Guided Practice Determine whether each of the following statements is always, sometimes, or never true. Explain. 1.Equiangular triangles are also acute? 2. Right triangles are acute. Always, equiangular triangles have 3 acute angles. Never, right triangles have one right angle and acute triangles have all acute angles.

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