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Test Review 4.2 Geometry Review for Test Sections 6.2. & 6.4 – 6.6 Name____________________________ I. Facts you need to know!! Kites Trapezoids Definition-a quadrilateral with one pair of parallel sides. The consecutive angles between the bases of a trapezoid are supplementary. In an Isosceles trapezoid the non-parallel sides are congruent and both sets of base angles are congruent. The diagonals of an isosceles trapezoid are congruent. Midsegment of a Triangle Definition-a segment that joins the midpoints of two sides of a triangle. The midsegment of a triangle is parallel to the third side. The midsegment of a triangle is one-half the length of the third side. The three midsegments of a triangle divide the triangle into four congruent triangles. Midsegment of a Trapezoid Definition-a segment joining the midpoints of the nonparallel sides. The midsegment of a trapezoid is parallel to the bases. The midsegemnt of a trapezoid is equal in length to the average of the two base lengths. Parallelograms Definition-a quadrilateral with both pairs of opposite sides parallel. The opposite angles are congruent. The consecutives angles are supplementary. The opposite sides are congruent. The diagonals bisect each other. Rhombuses Definition-a parallelogram with all four sides congruent. (remember it has all the qualities of a parallelogram) The diagonals are perpendicular to each other. The diagonals bisect the angles of the rhombus. Rectangles Definition-a quadrilateral with both pairs of opposite sides parallel and congruent and four right angles. (remember it has all the qualities of a parallelogram) The diagonals are congruent. The diagonals bisect each other. Squares Definition-a rectangle with all four sides congruent. (remember it has all the qualities of a parallelogram) The diagonals are congruent. The diagonal are perpendicular bisectors of each other. The diagonals bisect the angles. Definition- a quadrilateral with two sets of consecutive sides that are congruent The diagonals of a kite are perpendicular. The diagonal connecting the vertex angles of a kite is perpendicular bisector of the other diagonal. The non-vertex angles of a kite are congruent. The vertex angles of a kite are bisected by a diagonal. 1 2 3 7 4 6 5 II. Name the shapes pictured in the above box. III. True or False 1 .__________________________ ________1. A trapezoid is a parallelogram. 2. __________________________ ________2. If a quadrilateral is not a parallelogram, then the opposite sides are not congruent. 3. _________________________ ________3. Every rectangle is a square. 4. _________________________ 5. _________________________ ________4. A parallelogram with perpendicular diagonals is a rhombus or a square. 6. _________________________ ________5. The diagonals in a kite are perpendicular. 7. __________________________ ________6. All quadrilaterals have five sides. B A IV. Refer to ABCD to answer questions #1-6 1. AB // ____________ 2. DC = __________ 3. m A = ___________ 4. OA = ___________ 5. DO = ___________ 6. AD = ___________ O D C 7. A park in the shape of a quadrilateral PQRS is bordered by four sidewalks. Find the measure of each exterior angle of the park. P (8x)0 Q 0 (14x) (7x)0 S WXYZ is a parallelogram. Find each measure 8. WX = _______ 9. YZ = ________ 10. m X = _______ (11x)0 R 11. m W = _______ 12. Three vertices of parallelogram ABCD are A(-3, 1), B(5, 7), and C(6, 2). Find the coordinates of vertex D. Use figure to the right for 13 and 14. GHJK is a rhombus. Find each measure. 13. HJ = _______ 14. if m JLH = (4b – 6)o and m JKH = (2b + 11)o, find each measure. m HJG = _______ m GHJ = _______ In kite EFGH, m FHG = 68o, and m HEF = 62o. Find each measure. 15. m FEJ = _______ 16. m EHJ = _______ 17. m FGJ = _______ 18. m EHJ = _______ 19. A dulcimer is a trapezoid-shaped stringed instrument. The bases are 43 in. and 23 in. long. If a string is attached at the midpoint of each leg of the trapezoid, how long is the string? Draw a picture and label the drawing How long is the string? ________________ _________________________ Use figure to the right for 20 and 21.Determine if the conclusion is valid. If not tell what additional information is needed to make it valid. 20. Given: AB // CD , AB CD , AC BD Conclusion: ABCD is a square. B C A D _______________________________________________________________________________________ _______________________________________________________________________________________ 21. Given: AB CD , BC AD , BA AD Conclusion: ABCD is a rectangle. _______________________________________________________________________________________ _______________________________________________________________________________________ 22. SQUARE A 5x - 17 B 23. RECTANGLE D 3x - 5 550 C D E AB = _______ mDCA =_____ 25. RHOMBUS perimeter = 82 cm R 0 y 72 4 3 1 2 F 0 36 T A 420 w0 D 270 C 3x Z WZ = _____ 4x E x = _____ w = _____ mABC =______ D 0 63 22 ft F x= _____ y = _____ z = _____ 2y + 12 Y 27. ISOSCELES TRAPEZOID perimeter = 100 ft. B x0 W x = _____ S x 24. PARALLELOGRAM 5y - 3 X 9 m1=_____ m2 = _____ m3 = _____ m4 = _____ 26. KITE z+3 Q G (9y)0 G 3x - 7 ED = ______ mDEF = ______