Classifying Triangles

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Presentation transcript:

Classifying Triangles By angles Acute- all angle measures < 90 Obtuse- one angle measure > 90 Right- one angle = 90 Equiangular- all angle measures are equal By sides Scalene- no two sides are congruent Isosceles- at least two sides are congruent Equilateral- all sides are congruent

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 1-1a

Answer: ABC is acute. ACD is obtuse. ADE is right. 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 1-1b

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

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 1-2b

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

Since KLM is equilateral, each side has the same length. So 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 1-3a

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

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

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

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

Answer: ; since all 3 sides have different lengths, ABC 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. Example 1-4c