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4-1 Classifying Triangles

4-1 Classifying Triangles. You measured and classified angles. Identify and classify triangles by angle measures. Identify and classify triangles by side measures. Definition. A triangle is a figure formed by three line segments that connect three noncollinear points. C. vertex. Side.

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4-1 Classifying Triangles

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  1. 4-1 Classifying Triangles You measured and classified angles. • Identify and classify triangles by angle measures. • Identify and classify triangles by side measures.

  2. Definition A triangle is a figure formed by three line segments that connect three noncollinear points. C vertex Side Side A B vertex Side vertex

  3. Naming a triangle A triangle is named using its vertices and a ∆ symbol. This triangle can be named ∆ ABC C A B

  4. Classifying Triangles • Triangles can be classified in two ways – by their angles or by their sides. • All triangles have at least two acute angles, but the third angles is used to classify the triangle.

  5. Triangle Classification by Angles Acute 3 acute angles . Right One right angle. Obtuse One obtuse angle. Equiangular 3 congruent acute angles.

  6. A. Classify the triangle as acute, equiangular, obtuse, or right. Answer:The triangle has three congruent angles. It is an equiangular triangle.

  7. B. Classify the triangle as acute, equiangular, obtuse, or right. Answer:One angle of the triangle measures 130°, so it is an obtuse angle. The triangle has an obtuse angle, so it is an obtuse triangle.

  8. A. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔACD. A. acute B. equiangular C. obtuse D. right

  9. Classify ΔXYZ as acute, equiangular, obtuse, or right. Explain your reasoning. Point W is in the interior of XYZ, so by the Angle Addition Postulate, mXYW + mWYZ = mXYZ. By substitution, mXYZ = 40 + 50 = 90. Answer:Since ΔXYZ has a right angle, it is a right triangle.

  10. Triangle Classification by Sides Scalene no sides congruent. E B H A C G I Equilateral All sides congruent. D F Isosceles two sides congruent.

  11. Try ItClassify each triangle using both angle and side classification.

  12. ARCHITECTUREThe triangle truss shown is modeled for steel construction. Classify ΔJMN, ΔJKO, and ΔOLNas equilateral, isosceles, or scalene. Answer:ΔJMN has no congruent sides, so it is a scalene triangle. ΔJKO has no congruent sides, so it is a scalene triangle. ΔOLN has all sides congruent, so it is an equilateral triangle.

  13. ARCHITECTURE The frame of this window design is made up of many triangles. Classify ΔABC. A.isosceles B.equilateral C.scalene D.right

  14. If point Y is the midpoint of VX, and WY = 3.0 units, classify ΔVWY as equilateral, isosceles, or scalene. Explain your reasoning. By the definition of midpoint, VY = YX. VY + YX = VX Segment Addition Postulate VY + VY = 8.4 Substitution 2VY = 8.4 Simplify. VY = 4.2 Divide each side by 2. So, VW = 4.5 units, WY = 3.0 units, and VY = 4.2 units. Answer:Since all three sides have different lengths, the triangle is scalene.

  15. If point C is the midpoint of , classify ΔABC as equilateral, isosceles, or scalene. A.equilateral B.isosceles C.scalene

  16. ALGEBRA Find the measures of the sides of isosceles triangle KLM with base KL. __ Step 1Find d. KM = ML Given 4d – 13 = 12 – d Substitution 5d – 13 = 12 Add d to each side. 5d = 25 Add 13 to each side. d = 5 Divide each side by 5. Step 2Substitute to find the length of each side. KM = 4d – 13 Given = 5 + 6 or 11 d = 5 = 4(5) – 13 or 7 d = 5 ML = KM Given = 7 KM = 7 KL = d + 6 Given Answer: KM = ML = 7, KL = 11

  17. What is a triangle? A figure formed by three line segments that connect three noncollinear points. • What is the sum of the measures of the interior of any triangle? The sum of the measures of the angles of a triangle is 180° • How are triangles classified and named? Triangles are classified by sides and angles. Sides: scalene, isosceles and equilateral. Angles: acute, obtuse, right and equiangular.

  18. 4-1 Assignment Page 240, 15 -20, 22-36 even, 40 - 42

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