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Part 1 Unit 4-Review Part 1- Triangle Theorems and Rules Name of Theorem or relationship 1. Side angle relationship In words/ Symbols Diagrams/ Hints/ Techniques The longest side is across from the largest angle. The medium length side is across from the medium-sized angle. The shortest side is across from the smallest angle 2. Triangle inequality Theorem The sum of the lengths of the two smaller sides of a triangle is greater than the length of the largest side. To find an inequality of possible sides, add two given sides, subtract them. 3. Pythagorean Theorem a) c2 = a2 + b2 hypotenuse) a) To find a missing side b) If c2 < a2 + b2 it is acute If c2 > a2 + b2 it is obtuse If c2 = a2 + b2 it is right Draw arrows! Add up the two smaller sides and compare to the largest side. If the sum is greater, it’s a triangle! 2,3,4 (2+3) > 4 ? yes! C is longest side ( b) to Classify triangles If you see a right angle, it’s a right triangle! use P.T to solve for a missing side. WATCH OUT! If asked “does this make a triangle” you must use Theorem # 2NOT PYTHAGOREAN. ERROR ALERT: you must SQUARE (power of 2) a, b and c, DIFFERENT FROM Theorem #2 seen above. 4.Isosceles triangle Theorem The base angles of an isosceles triangle are equal in measure. The sides opposite the base angles in an isosceles triangle (called legs) are equal in length. Angles opposite are congruent! If you see expressions, make them equal to each other! 5. Exterior angle theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle. IN + IN =OUT Part 1 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, m∡D = 400 , m∡O= 600 ,, and m∡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. Part 1 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) Given the following information find the degrees in each angle of the triangle. <ABC = ________________ <BCA = ________________ <BAC = _______________ What is the longest side of the triangle? ___________________________ 7) Determine whether the following sides form a right , acute or obtuse triangle. Justify your answer with words. a) 5, 11, 12 Part 1 b) 5, 12, 13 c) 7, 15, 18 8) Solve for x . Give 9) your answer in the simplest radical form. 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) mABC mD (3) mÐABC > mÐC (4) mÐABC > mÐC + mÐD 10) 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. Part 1 11) Part 1 12). Consider the following diagram with 2 right triangles labeled, and the sides included in the diagram. Solve for the whole length of side AC.