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Transcript
4.1 Classifying Triangles Objectives Identify and classify triangles by angles Identify and classify triangles by sides Parts of a Triangle 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 Side opposite A C Classifying Triangles by Angles One way to classify triangles is by their angles… Acute Obtuse all 3 angles are acute 1 angle is obtuse (measure < 90°) (measure > 90°) Right 1 angle is right (measure = 90°) An acute ∆ with all angles is an equiangular ∆ . Example 1: ARCHITECTURE The triangular truss below is modeled for steel construction. Classify JMN, JKO, and OLN as acute, equiangular, obtuse, or right. 60° 60° Example 1: 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. Classifying Triangles by Sides Another way to classify triangles is by their sides… Equilateral 3 congruent sides Isosceles Scalene 2 congruent sides no congruent sides Example 2a: Identify the isosceles triangles in the figure if Isosceles triangles have at least two sides congruent. Answer: UTX and UVX are isosceles. Example 2b: 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. Example 2c: Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, EBC, DEB, DCE, ADC, ABD Example 3: 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 5=d Example 3: Next, substitute to find the length of each side. KL = 7 LM = 7 KM = 7 Answer: For KLM, and the measure of each side is 7. Your Turn: ALGEBRA Find x and the measure of each side of equilateral triangle if and Answer: Example 4: COORDINATE GEOMETRY Find the measures of the sides of RST. Classify the triangle by sides. Example 4: Use the distance formula to find the lengths of each side. Answer: ; since all 3 sides have different lengths, RST is scalene. Assignment Geometry: Pg. 181 #5 – 18, 22 – 26, 32 Pre-AP Geometry: Pg. 181 #13 – 18, 22 – 26, 32, 34, 38