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Geometry B Name: ______________________ Date: ____________ Block: ____________ Triangle Congruence Chapter 4 Review All work must be shown for credit. Sections 4.1 - 4.6 and 4.8. Define the following terms: acute triangle auxiliary line base angle congruent polygons corresponding angles corresponding sides CPCTC equiangular triangle equilateral triangle exterior angle included angle included side interior angle isosceles triangle legs of an isosceles triangle obtuse triangle remote interior angle right triangle scalene triangle triangle rigidity vertex angle Tell whether each statement is sometimes, always, or never true. Support your answer with a sketch. 22) An acute triangle is a scalene triangle. 23) A scalene triangle is an obtuse triangle. 24) An equiangular triangle is an isosceles triangle. 2 25) Classify each triangle by its angle measures. △BEA 26) Classify each triangle by its side lengths. △PST △RSP △DBC △ABC △RPT 27) Find the side lengths of each triangle. 28) An isosceles triangle has a perimeter of 34 cm. The congruent sides measure (4x - 1) cm. The length of the third side is x cm. What is the value of x? 3 29) The base of the Flatiron Building is a triangle bordered by three streets: Broadway, Fifth Avenue, and East Twenty-Second Street. The Fifth Avenue side is 1 ft. shorter than twice the East Twenty-second Street side. The East Twenty-second Street side is 8 ft. shorter than half the Broadway side. The Broadway side is 190 ft. a. Find the two unknown side lengths. b. Classify the triangle by its side lengths. 30) Find m∠S 31) Find m∠N. 4 32) Given: RS ≅ UT, and VS ≅ VT. V is the midpoint of RU. Prove: △RSV ≅ △UTV 33) Given: AB ≅ DE, DB ≅ AE Prove: △ADB ≅ △DAE 34) Show and explain that △ADB ≅ △CDB when s = 5. 5 35) Given: C is the midpoint of AG, HA GB Prove: ∆HAC ∆BGC 36) Given: WX ⊥ XZ , YZ ⊥ ZX , WZ YX Prove: ∆WZX ∆YXZ 6 37) Given: PQ RQ PS RS Prove: QS bisects ∠PQR 38) Given: E is the midpoint of AD and BC Prove: △ABE and △DCE 7 Indicate whether the two triangles shown are congruent by SSS, ASA, SAS, AAS or HL. If there is not enough information given, write “not possible”. 39) 40) 41) 42) 8 43) Find the m∠N and m∠P. 44) The measure of one of the acute angles in a right triangle is given What is the measure of the other acute angle? 56.8° 4y° 45) Find the measure of each angle. 46) For Triangle ABC and Triangle XYZ, mA = mX and mB = mY. Find the measure of C and Z if mC =(4x + 7)° and mZ = 3(x + 5) °. What theorem did you use to solve this problem? 9 47) Find the measure of all angles. 48) Find the length of BC. 49) A plane is flying parallel to the ground along AC. When the plane is at A, an air-traffic controller in tower T measures the angle to the plane as 0°. After the plane has traveled 2.4 mi to B, the angle to the plane is 80°. How can you find BT? smilardo.wordpress.com - homework: worksheets: link to book and more Follow me @MsMilardo 10