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SKILL #1 NON-NEGOTIABLE SKILL #1 The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13, the altitude is x, and the base is 10. Find the length of the altitude. 10 SKILL #2 NON-NEGOTIABLE SKILL #2 In the diagram below, What is and ? are shown with and . SKILL #3 NON-NEGOTIABLE SKILL #3 What is the measure of an interior angle of a regular octagon? What is the sum of the interior angles of the same octagon? SKILL #4 NON-NEGOTIABLE SKILL #4 In triangle ADC, Segment DE is the altitude of the triangle. AE = 5x EC= 4x +3 and mβ‘ π·πΈπ΄ = 5x +5. Solve for x. Name: _____________ Station 1: Angle Side Relationships and Triangle inequality Theorem Geometry Pd. ______ 1) In triangle RQS, RQ= 10 inches, SQ =9 inches and RS= 8 inches, arrange the angles form smallest to greatest. 2) The diagram at the right shows a right triangle with representations for two angles. What is the value of x? 3) In triangle DOG, mβ‘D = 400 , mβ‘O= 600 ,, and mβ‘G = 800 ,. State the longest side of the triangle __________________ State the shortest side of the triangle _________________ Classify the triangle based on its SIDES ___________________ 4) State whether each of the following could be the sides of a triangle and why. a) {6,6,6} b) {2,2,4} c) {5,9,10} d) {4,4,9} 5) Two sides of a triangle have lengths 2 and 7. Write an inequality for all possible integer lengths of the third side. 6) In the diagram below of quadrilateral ABCD with diagonal , and . If is parallel to , , , find m < π΄π΅π· , Name: _____ Geometry Pd. ____ 1) Station 2: Pythagorean, Isosceles Triangle and Exterior angle Theorems Given the following information find the degrees in each angle of the triangle. <ABC = ________________ <BCA = ________________ <BAC = _______________ What is the longest side of the triangle? ___________________________ 2) Determine whether the following sides form a right , acute or obtuse triangle. Justify your answer with words. a) 5, 11, 12 3) b) 5, 12, 13 c) 7, 15, 18 4) Solve for x . Give your answer in the simplest radical form. 5) In the diagram below of DBCD , side DB is extended to point A. (Note: The diagram above is not drawn to scale) Which statement must be true? (1) mÐC > mÐD (2) mοABC οΌ mοD (3) mÐABC > mÐC (4) mÐABC > mÐC + mÐD 6) In a triangle, the ratio of the angles is 1:3:5. Find the measure of all the angles and Classify the triangle according to its angles. Name: ________ Station 3: Points of concurrency and Exterior/Interior angles in polygons. Geometry Pd. ______ 1) Using the inferences provided, identify each of the segments as one of the following for ΞπΆπ΅π΄: Altitude, Median, angle bisector, or perpendicular bisector. B a. Given: Μ Μ Μ Μ π΅π· β₯ Μ Μ Μ Μ π΄πΆ Μ Μ Μ Μ must be a(n) π΅π· G A b. Given: Μ Μ Μ Μ π΄πΈ β Μ Μ Μ Μ πΈπΆ Μ Μ Μ Μ must be a(n) π΅πΈ c. Given: β‘π΄π΅πΉ β β‘πΆπ΅πΉ Μ Μ Μ Μ π΅πΉ must be a(n) E F D C Μ Μ Μ Μ β₯ π΄πΆ Μ Μ Μ Μ πππ Μ Μ Μ Μ Μ Μ Μ Μ d. Given πΊπΈ π΄πΈ β πΈπΆ Μ Μ Μ Μ πΊπΈ must be a(n) 2) Adrian thinks the segment NK in the following triangle is an altitude while Daniel thinks itβs a median. Is Adrian correct? IS Daniel correct? Are they both correct? Are they both incorrect? EXPLAIN! 3) Find the coordinates of the centroid of the triangle with the given vertices. J(β1, 2), K(5, 6), L(5, β2) 4) Find one of the exterior angles of a regular decagon. 5) Find the measure of one interior angle of a regular nonagon (9 sides). 6) Find the number of sides of a polygon whose sum of interior angles in 1620°. 7) a. Circle the point of concurrence that is formed when 2 or more altitudes intersect. Centroid Orthocenter Incenter Circumcenter a. Where could this point be located? ( circle all that apply) Inside the triangle outside the triangle 8) On the triangle a. Circle the point of concurrence that is formed when 2 or more medians intersect. Centroid Orthocenter Incenter Circumcenter a. Where could this point be located? ( circle all that apply) Inside the triangle outside the triangle On the triangle Μ Μ Μ Μ Μ and Μ Μ Μ Μ 9) In triangle ABC, Μ Μ Μ Μ Μ π΄π·, πΆπΉ, π΅πΈ are medians. If Μ Μ Μ Μ πΆπΉ = 33, find CG and FG.