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Transcript
Geometry/Trig Name: ______________________________ Date: _______________________________ Lesson 13-2: Final Exam Review [Unit 3 Angles and Triangles] 1. 2. 3. 4. 5. 6. 7. The learning goals we achieved in these units were… What are right, acute, and obtuse angles? How can we use special angle pair definitions to solve for missing angles? How do you classify the different types of triangles by sides? What is the Side-Angle Relationship in triangles? What is the Triangle Inequality Theorem? What does the Triangle Inequality Theorem help us to conclude? What is the Pythagorean Theorem? For which type of triangle does the Pythagorean Theorem apply? What is the isosceles triangle theorem Key Ideas: The Pythagorean Theorem What is the Pythagorean Theorem? What does each letter represent? Side-Angle Relationship --The ___________side is across from the______________ angle. --The ______________ side is across from the ______________ angle. --The ______________ side is across from What type of triangles do we use this with? the ______________ angle. Isosceles Triangles Triangle Properties --All angles in a triangle add to __________. Isosceles triangles are triangles with two congruent ______________. How do we identify which two angles are congruent to each other? --Classifying but sides: Scalene ( _____ sides are congruent) Equilateral( _____ sides are congruent) Isosceles( _____ sides are congruent) Triangle Inequality: The sum of the two _________________________ Sides must be _______________________ than the third side. --Classifying by angles: Acute (all angles are __________ 90) Obtuse (one angle is __________ 90) Right (one angle is __________ 90) Geometry/Trig Concept Diagram Vertical angles Supplementary Angles Complementary Angles Adjacent Angles Angles at a Point Definition Two angles ____________________ each other when 2 lines _______________. Two angles that add to _______________. Two angles that add to _______________. Two angles who share a common ________ and a common ________ (“next to”) Angles where all vertices share the same ___________. Their sum is ____________. Guided Example: Find the missing side of the triangle: 1) a = 5, b = x, c = 13 (c is always the hypotenuse) 2) . c2 = a2 + b2 132 = 52 + x2 169 = 25 + x2 x2 = 144 √𝑥 2 = √144 x = 12 Steps: 1) Identify the measure of each side length and classify them as a, b, or c. 2) Use the Pythagorean Theorem and properties of Algebra to find the missing side. 3) Put your answer in simplest radical form, if applicable. Geometry/Trig Practice Section by Topic: Types of Angles: 1. Type of Angles: _____________________________________ b = ______________∘ 2. Type of Angles: _____________________________________ b = ______________∘ 3. Type of Angles: _____________________________________ b = ______________∘ 4. Type of Angles: _____________________________________ b = ______________∘ 5. Type of Angles: _____________________________________ b = ______________∘ Geometry/Trig Properties of Triangles: 6. What is the measure of ∠𝐶? 7. In ∆ABC, m∠A = 42° and m∠C = 63°. What is the measure of ∠B? 8. In ∆ABC, m∠A = x° and m∠B = 2x+2° and m∠C = 3x+4°, what is the measurement of ∠B? Classifying Triangles: Classify the following triangles according to their sides. 7 This triangle is a __________________ triangle, because it has _____________________________ This triangle is a __________________ triangle, because it has _____________________________ This triangle is a __________________ triangle, because it has _____________________________ This triangle is a __________________ triangle, because it has _____________________________ Geometry/Trig 9. In triangle ABC, m<A = 35°, and m<C = 110°. What type of triangle is triangle ABC in terms of its SIDES? How do you know? 10. Given Triangle ABC, 𝑚∡A = 30°, 𝑚∡B = 2x°, 𝑚∡C = 70° find the measurement of angle B. a. What is the largest side of triangle ABC? The largest side of triangle ABC is _______________ because ___________________________________ b. Is triangle ABC acute, obtuse, or right? Triangle ABC is __________________________ because _____________________________________ Isosceles Triangle Theorem: 11. What type of triangle is this? How do you know? a. Solve for the value of x 12. What type of triangle is this? How do you know? a. Solve for the value of y. Geometry/Trig 13. In triangle XYZ, side XZ is extended to point p outside of the triangle. Solve for the angle marked b. Explain your steps. I know angle Y = ________ because … I know ∠𝑌𝑍𝑋 = _______ because… I know ∠𝑃𝑍𝑌 = ______ because… 14. The accompanying diagram shows the roof of a house that is in the shape of an isosceles triangle. The vertex angle formed at the peak of the roof is 86°. What is the measure of angle x? Explain how you know. Triangle Inequality Theorem: For each of the following, determine if the side lengths given can form a triangle? 15. 17. 7, 5, 4 5, 2, 4 16. 18. 3, 6, 2 4ft, 108 in., 9 ft. Geometry/Trig Pythagorean Theorem: 19. If (16, 30, y) are the sides of a right triangle, where y is the largest side, what is the value of y? Leave your answer in simplest radical form, if necessary. 20. Solve for the length of side BC? Leave your answer in simplest radical form. 21. Does this triangle have a right angle? Explain how you know. 22. a) In ∆ABC, m∠A = x° and m∠B = 2x+2° and m∠C = 3x+4°, what is the value of x? b) According to its angles, what type of triangle is this? c) What side of ∆ABC is the shortest? How do you know?