NAME ________________________
PER _______
DATE _______________________
ID: A
PreAP Geometry Unit 6 Review Quadrilaterals 1 The regular polygons below form a pattern.
What equation could be used to find the perimeter,P, of an n-gon in the pattern? A P = n(n-1) C P = n 2 - n +1 B P = 2n D P = 8n - 19 2 Sketch each polygon described below. If the sketch cannot be made write impossible.
3 Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: a concave polygon Conjecture: It can be regular or irregular. A False; to be concave the angles cannot be congruent. B True C False; all concave polygons are regular. D False; a concave polygon has an odd number of sides.
A. a concave equilateral hexagon
B. a convex regular hexagon
C. a concave regular hexagon
4 Find the sum of the measures of the interior angles of a convex 45-gon.
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5 Find the sum of the measures of the exterior angles of a convex 39-gon.
8 Determine whether the following quadrilaterals are parallelograms. Justify your answer.
__________ _______ 6 If the measure of each exterior angle of a regular polygon is 72, find the measure of each interior angle.
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List the 3 other ways quadrilerials can be proven parallelograms.
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7 A convex pentagon has interior angles with measures (5x - 12)°, (2x + 100)°, (4x + 16)°, (6x + 15)°, and (3x + 41)°. Find x.
____________________________ ____________________________ ____________________________
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Complete the statement about parallelogram ABCD.
9 ÐACD @ A ÐBAC ; Opposite angles of parallelograms are congruent. B ÐBAC ; Alternate interior angles are congruent. C ÐBDC ; Alternate interior angles are congruent. D ÐBDC ; Opposite angles of parallelograms are congruent. 10 ÐDAB @ F ÐBCD; Alternate interior angles are congruent. G ÐABC ; Opposite angles of parallelograms are congruent. H ÐBCD; Opposite angles of parallelograms are congruent. J ÐABC ; Alternate interior angles are congruent.
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11 For rhombus GHJK, find mÐ1.
15 For isosceles trapezoid MNOP, find mÐMNP.
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12 For rhombus GHJK, find mÐ1.
16 Given trapezoid ABCD with median EF, which the following is true?
F
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G H
13 Use square ABCD to the following measures.
J
1 AD 2 AE = FD AB = EF BC + AD EF = 2 EF =
17 For isosceles trapezoid PQRS, L and M are the midpoints of the legs. Find LM and mÐR.
mÐAED =_ _ _ _ _ _ _ mÐEDA =_ _ _ _ _ _ _ _______ 14 The length of one base of a trapezoid is 19 inches and the length of the median is 16 inches. Find the length of the other base.
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of
18 Determine whether the quadrilateral ABCD with vertices A(10, 2), B(10, 6), C(-4, 6), and D(-4, 2) is a rectangle. Justify your answer.
20 Given an isosceles trapezoid, find the coordinates of point C.
__________ 21 Determine wearther statement (3) is a valid conclusion of statements (1) and (2)? (1) If a figure has 4 right angles, then the figure is a rectangle. (2) A rectangle has 2 pairs of parallel sides. (3) If a figure has 4 right angles, then the figure has 2 pair of parallel sides. _________ _____________ 22 Find the measure of each interior angle.
1 19 If the slope of AB is , the slope of BC is -4, and 2 1 the slope of CD is , find the slope of DA so that 2 ABCD is a parallelogram. ________
____________ , _______________ ____________ , _______________
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23 Find each of the following measures;
25 Complete the following proof. Given: HJ K L is a rectangle. M is the midpoint of HJ . Prove: LM @ KM
m
WID = _______
perimeter of kite WIND = _______ Write true or false. 24 a) A parallelogram always has four right angles. _______
26 If KLMN is a parallelogram, find the value of x, y, and the length of segment LJ.
b) The diagonals of a rhombus always bisect the angles. _______ c) A rhombus is always a square. _______ d) A rectangle is always a square. _______ e) The diagonals of an isosceles trapezoid are always congruent. _______
__________, ___________, ___________
f) The median of a trapezoid always bisects the angles. _______
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27 Find the measure of each interior angle.
__________, __________, __________, __________. 28 Optional: Given a parallelogram, find x and y.
__________, __________
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ID: A
PreAP Geometry Unit 6 Review Quadrilaterals Answer Section 1 A 2 A.
B.
3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 21
C. Not possible A 7740 360 108 19 Yes: Diagonals bisect each other. Both pairs of opp. sides are @ . Both pairs of opp. sides € One pair of sides @ and € Both pairs of opposite angles @ B J 68 38 90, 45 13 inches 64 J 37, 123 Yes; AB ^ BC, BC ^ CD, CD ^ AD, so all Ðs are rt. Ðs. -4 C(a + b, c) yes 1
ID: A 22 44, 101, 102, 113 23 90, 16, 26 24 a) false b) true c) false d) false e) true f) false 25 Given: H J K L is a rectangle. M is the midpoint of HJ . Prove: LM @ KM Proof: Statement 1. H J K L is a rectangle; M is the midpoint of HJ . 2. H J K L is a parallelogram. 3. KJ @ LH 4. ÐJ and ÐH are right angles. 5. ÐJ @ ÐH 6. HM @ MJ 7. DMLH @ DMKJ 8. LM @ KM 26 x = 4, y = 11, LJ = 26 27
Reason 1. Given 2. Definition of rectangle 3. Opposite sides of parallelograms are congruent. 4. Definition of rectangle 5. All right angles are congruent. 6. Midpoint Theorem 7. SAS 8. CPCTC
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