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Geometry/Trig Relationships in Triangles GSP Lab - Answers Name: __________________________ Date: ___________________________ Scalene Triangle – A triangle with no congruent sides. Sketch a picture of the scalene triangle that you created in Sketchpad. Fill in all angle measurements and segment lengths. Are any of the angle measures the same? No Which side is longest? ___________________________________ Which angle is largest? __________________________________ Which side is shortest? _________________________________ Which angle is smallest? _________________________________ What is the relationship between the position of the longest side and the Scalene Triangle largest angle? They are across from one another. What is the relationship between the position of the shortest side and the smallest angle? They are across from one another. Ex1 – List the angle measurements in order from smallest to largest. Ex2 – List the side lengths in order from shortest to longest. (Diagram NOT drawn to scale!) (Diagram NOT drawn to scale!) K Q 12cm 5cm 32 ° R J 14cm 85 ° 63 ° P L L, J, K RP, RQ, QP Go to my website and find Unit 3 to check your examples. When you are ready to take the check for understanding quiz called “Scalene Triangle” through Quia. Isosceles Triangle – A triangle with two congruent sides. Turn to page 134 of a textbook. Read the paragraph under the heading 4-4 The Isosceles Triangle Theorems and complete the first four lines of the fill in notes below: The congruent sides of the Isosceles Triangle are called the legs. The third side is called the base. The two angles across from the legs are called the base angles. The angle across from the base is called the vertex angle. Which angles are the base angles in your sketch? A and C What is interesting about the measures of the base angles? They are congruent. Try to complete the following Theorem: The base angles of an isosceles triangle are congruent. Don’t worry, we’ll prove this theorem during unit 4. Go to my website and find Unit 3 to check your examples. When you are ready to take the check for understanding quiz called “Isosceles Triangle” through Quia. Isosceles Triangle p. 134 of book Sketch a picture of the isosceles triangle provided for you in Sketchpad. Fill in all angle measurements and segment lengths. Geometry/Trig Relationships in Triangles GSP Lab - Answers Name: __________________________ Date: ___________________________ Equilateral Triangle – A triangle with three congruent sides. What is true about all three side lengths? All three sides have equal lengths. Sketch a picture of the equilateral triangle that you created in Sketchpad. Fill in all angle measurements and segment lengths. What is true about all three angle measures? All three angle measures are equal. They are all 60 degrees. Equilateral Triangle Corollary 1 (p. 135): An equilateral triangles is also equiangular. Corollary 2 (p. 135): An equilateral triangle has three 60 degree angles. Example 3: A 5x + 2 B mB = 60 60° 10x - 14 5x + 2 = 10x – 14 16 = 5x x = 16/5 = 3.2 C mC = 60 x = 16/5 = 3.2 AB = 5(16/5) + 2 = 18 AC = 18 BC = 10(16/5) – 14 = 18 Go to my website and find Unit 3 to check your examples. When you are ready to take the check for understanding quiz called “Equilateral Triangle” through Quia. Diagrams for Quia Quizzes (Diagrams are NOT drawn to scale): Diagram 1 A Diagram 2 J 60° 4in B 80° 40° M Diagram 3 100° 40° N C K Diagram 4 10in L 12in S Q 18in 12in R 12in P