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Honors Geometry Unit 2B Review Quads To be successful on this exam you need to have mastered the following concepts. Understand the triangle inequality theorems and hinge theorem. Use the triangle midsegment theorem to find lengths. Find angle measures in isosceles and equilateral triangles. Understand perpendicular bisectors and their points of concurrency. Understand medians and their points of concurrency. Know how to find a point equidistant from the sides or angles of a triangle. Know properties of quadrilaterals. – parallelograms, rectangles, rhombi, squares, trapezoids, isosceles trapezoids, and kites. HANDOUT! Classify special quadrilaterals – using given properties and coordinate proof. Find angle measures of special quadrilaterals – give properties to justify your answers. Know and use the trapezoid midsegment theorem. Know methods to prove that a given quadrilateral is a parallelogram, rectangle, rhombus or square. HANDOUT! Learning Targets 13-1-1 Prove theorems about angle measures in triangles. 13-1-2 Apply theorems about angle measures in triangles. 13-2-2 Prove and use theorems about isosceles triangles. 14-1-1 Determine the point of concurrency of the altitudes of a triangle. 14-1-2Use the point of concurrency of the altitudes of a triangle to solve problems. 14-2-1 Determine the point of concurrency of the medians of a triangle. 14-2-2 Use the point of concurrency of the medians of a triangle to solve problems. 14-3-2 Use the points of concurrency of the perpendicular bisectors and the angles bisectors of a triangle to solve problems. 15-1-1 Develop and use properties of kites. 15-1-2 Prove and use the triangle midsegment theorem. 15-2-1 Develop properties of trapezoids. 15-2-2 Prove properties of trapezoids. 15-3-1 Develop properties of parallelograms. 15-3-2 Prove properties of parallelograms. 15-4-1 Develop properties of rectangles, rhombi, and squares. 15-4-2 Prove properties of rectangles, rhombi, and squares. 16-1-1 Develop criteria for showing that a quadrilateral is a parallelogram. 16-1-2 Prove that a quadrilateral is a parallelogram. 16-2-1 Develop criteria for showing that a quadrilateral is a rectangle. 16-2-2 Prove that a quadrilateral is a rectangle. 16-3-1 Develop criteria for showing that a quadrilateral is a rhombus. 16-3-2 Prove that a quadrilateral is a rhombus. 16-4-1 Develop criteria for showing that a quadrilateral is a square. 16-4-2 Prove that a quadrilateral is a square. Vocabulary Triangle Inequality Theorem Triangle Sum Theorem Isosceles Triangle Theorem Converse of the Isosceles Triangle Theorem Interior Angle Exterior Angle Remote Interior Angle Leg Base Base Angle Vertex Angle Triangle Exterior Angle Theorem Hinge Theorem Point of Concurrency Altitude Angle Bisector Median Perpendicular Bisector Orthocenter Centriod Circumcenter Incenter Centriod Theorem Midsegment Triangle Midsegment Theorem Trapezoid Midsegment Theorem Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Kite Consecutive Angles/Sides Opposite Angle/Sides diagonal Below are some problems for you to practice before the exam. Not every type of problem on the exam is represented here, however these problems will allow you to refresh your memory on some concepts that you will see on the exam. It is in your best interest to use your class notes and examples as well as homework problems to be fully prepared for the exam. 1.) An angle exterior to the vertex of an isosceles triangle measures 80 degrees. Find the measures of the base angles of the triangle. 2.) AB is a midsegment. Find the value of x. 3.) What is the most precise name for quadrilateral ABCD with vertices A(-5,2), B(-3,6), C(6,6) and D(4,2). Justify your answer using coordinate proof. 4.) 5.) The quadrilateral is a parallelogram. Find the values of the variables. 6.) Given : ∡𝑆𝑉𝑈 ≅ ∡𝑇𝑆𝑈 𝑎𝑛𝑑 ∡𝑉𝑆𝑇 ≅ ∡𝑇𝑈𝑉 Prove : 𝑉𝑈 ∥ 𝑆𝑇 V U X S T 7.) State the truth value of each of the following a. All quadrilaterals are rectangles. b. All quadrilaterals are squares. c. All rectangles are quadrilaterals. d. All quadrilaterals are parallelograms. e. All squares are rhombuses. f. All kites are quadrilaterals g. All rectangles are squares. h. All rhombuses are parallelograms. 8.) Find the measures of the angles 1, 2, and 3 in the kite below. Name the property you used to find each angle. 9.) What are the three ways to prove a parallelogram is a rhombus? 10.) What are the five ways to prove a quadrilateral is a parallelogram? 11.) Given :𝑉𝑈 ∥ 𝑆𝑇 𝑎𝑛𝑑 𝑉𝑈 ≅ 𝑆𝑇 Prove ∆𝑉𝑋𝑈 ≅ ∆𝑇𝑋𝑆 V U X S T 12.) Find the measures of the missing angles. Name the property you used to find each angle. 13.) 14.) A triangle has sides of 8 and 13. What is the range of values possible for the third side? 15.) For each figure below, solve for x.