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4.1 Classifying Triangles

4.1 Classifying Triangles. Objectives. Identify and classify triangles by angles Identify and classify triangles by sides. A triangle is a 3-sided polygon The sides of ∆ABC are AB, BC, and AC The vertices of ∆ABC are A, B, and C

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4.1 Classifying Triangles

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  1. 4.1 Classifying Triangles

  2. Objectives • Identify and classify triangles by angles • Identify and classify triangles by sides

  3. A triangle is a 3-sided polygon The sides of ∆ABC are AB, BC, and AC The vertices of ∆ABC are A, B, and C Two sides sharing a common vertex are adjacent sides The third side is called the opposite side All sides can be adjacent or opposite (it just depends which vertex is being used) A adjacent adjacent B C Parts of a Triangle Side opposite A

  4. Classifying Triangles by Angles One way to classify triangles is by their angles… Acuteall 3 angles are acute (measure < 90°) Obtuse1 angle is obtuse (measure > 90°) Right1 angle is right(measure = 90°) An acute ∆ with all angles  is an equiangular ∆ .

  5. Example 1: ARCHITECTURE The triangular truss below is modeled for steel construction. ClassifyJMN, JKO, and OLNas acute, equiangular, obtuse, or right. 60° 60°

  6. Example 1 cont: 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.

  7. Classifying Triangles by Sides Another way to classify triangles is by their sides… Equilateral3 congruent sides Isosceles2 congruent sides Scaleneno congruent sides

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

  9. Identify the scalene triangles in the figure if Example 3: Scalene triangles have no congruent sides. Answer:VYX, ZTX, VZU, YTU, VWX, ZUX, and YXU are scalene.

  10. Example 4: Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, EBC, DEB, DCE, ADC, ABD

  11. ALGEBRAFind d and the measure of each side of equilateral triangleKLMif and Since KLM is equilateral, each side has the same length. So Example 5: 5 = d

  12. Answer: For KLM, and the measure of each side is 7. Example 5 cont: Next, substitute to find the length of each side. LM = 7 KM = 7 KL = 7

  13. ALGEBRA Find xand the measure of each side of equilateral triangle if and Example 6: Answer:

  14. Example 7: COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides.

  15. Answer: ; since all 3 sides have different lengths, RST is scalene. Example 7 cont: Use the distance formula to find the lengths of each side.

  16. Assignment • Geometry: Pg. 180 #5 - 10, 13-18, 32 - 37

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