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Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240 Lesson 4-1 Classifying Triangles Lesson 4-2 Angles of Triangles Lesson 4-3 Congruent Triangles Lesson 4-4 Proving Congruence–SSS, SAS Lesson 4-5 Proving Congruence–ASA, AAS Lesson 4-6 Isosceles Triangles Lesson 4-7 Triangles and Coordinate Proof Example 1 Classify Triangles by Angles Example 2 Classify Triangles by Sides Example 3 Find Missing Values Example 4 Use the Distance Formula OBJECTIVE: To identify and classify triangles by angles (2.9.8D) (M8.C.1.1) ARCHITECTURE The triangular truss below is modeled for steel construction. Classify JMN, JKO, and OLN as acute, equiangular, obtuse, or right. 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. 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. Identify the isosceles triangles in the figure if Isosceles triangles have at least two sides congruent. Answer: UTX and UVX are isosceles. Identify the scalene triangles in the figure if Scalene triangles have no congruent sides. Answer: VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene. Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, EBC, DEB, DCE, ADC, ABD 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. Next, substitute to find the length of each side. Answer: For KLM, and the measure of each side is 7. ALGEBRA Find d and the measure of each side of equilateral triangle if and Answer: COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides. Use the distance formula to find the lengths of each side. Answer: ; since all 3 sides have different lengths, RST is scalene. 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? Always, equiangular triangles have 3 acute angles. 2. Right triangles are acute. Never, right triangles have one right angle and acute triangles have all acute angles. Click the mouse button or press the Space Bar to display the answers. End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.