Download 6.5 Identifying Quadrilaterals

Name ______________________________________ Period ______
1) A rectangle is NOT always a…
A. parallelogram
B. quadrilateral
C. square
D. polygon
6.5 Identifying Quadrilaterals
2) Quadrilateral TOPS is a parallelogram. If its opposite angles are
supplementary, what statement must be true?
A. Quadrilateral TOPS is a trapezoid.
B. Quadrilateral TOPS is a square
C. Quadrilateral TOPS is a rhombus
D. Quadrilateral TOPS is a rectangle
3) A rhombus is also a…
4) ZUMO is a kite with diagonals UO and ZM that intersect at G. Which of
the following statements must be true?
A. kite
B. parallelogram
C. square
D. rectangle
A. ΔZUM is an acute triangle.
B. ΔZOM is an isosceles triangle.
C. ∠UGM is a right angle
D. ∠UZO is a right angle
5) HAMR is a parallelogram with diagonals HM and RA
the intersect at T. Which of the following statements
must be true?
̅̅̅ and ̅̅̅̅
6) JUNE is a rectangle with diagonals ̅𝐽𝑁
𝐸𝑈 that
intersect at point L. Which of the following statements is
false?
A. ̅̅̅
𝐽𝑈 || ̅̅̅̅
𝐸𝑁
B. ΔJUL≅ΔNLE
C. 𝛥𝑈𝑁𝐿 ≅ 𝛥𝐽𝐸𝑈
̅̅̅ ≅ ̅̅̅̅
D. ̅𝐽𝑁
𝐸𝑈
A. ∆𝑅𝐴𝑀 is an obtuse triangle.
B. 𝛥𝐻𝐴𝑅 ≅ 𝛥𝑀𝑅𝐴
̅̅̅̅
̅̅̅̅ ≅ 𝑇𝐴
C. 𝐻𝑇
D. 𝛥𝐻𝑇𝐴 ≅ 𝛥𝑀𝑇𝐴
7) “If at least one pair of opposite sides are congruent, then the quadrilateral is a parallelogram.”
Which of the following provides a counterexample to the statement above?
A.
B.
C.
8) Polygon THIS is a quadrilateral. If only one pair of
opposite angels are congruent, which of the following
statements is true?
D.
̅̅̅ that
9) WIFY is a rhombus with diagonals ̅̅̅̅̅
𝑊𝐹 and 𝑌𝐼
intersect at E. Which of the following statements must be
true?
A. Polygon THIS is a rectangle
B. Polygon THIS is a trapezoid
C. Polygon THIS is a parallelogram
D. Polygon THIS is a kite
̅̅̅̅̅ ≅ 𝐸𝐼
̅̅̅
A. 𝑊𝐸
̅̅̅̅̅ ⊥ ̅̅̅̅
B. 𝑊𝑌
𝑌𝐹
C. ̅̅̅̅̅
𝑊𝐹 bisects ∠𝐼𝐹𝑌
D. ̅̅̅̅̅
𝑊𝐹 ≅ ̅̅̅
𝑌𝐼
10) “If one pair of opposite angles of quadrilateral are
11) Which figure can serve as a counterexample to the
conjecture below?
congruent, then the quadrilateral is a parallelogram.”
Which figure can serve as a counterexample to the
conjecture above?
A. Isosceles Trapezoid
B. Rhombus
C. Kite
D. Square
“If two pairs of angles are congruent in a quadrilateral, then
the quadrilateral is a parallelogram.”
A. Rectangle
B. Trapezoid
C. Kite
D. Isosceles trapezoid
12) Quadrilateral BAKR is a parallelogram. The adjacent
angles are congruent and the diagonals are
perpendicular. What statement must be true?
A. Quadrilateral BAKR is a rectangle
B. Quadrilateral BAKR is a square
C. Quadrilateral BAKR is a rhombus
D. Quadrilateral BAKR is a isosceles trapezoid
14) Find the area of △ 𝐵𝑀𝐼 in the square BITS.
B
I
M
̅̅̅̅ and ̅̅̅̅
13) FATY is a parallelogram with diagonals 𝐹𝑇
𝑌𝐴 that
intersects at O. Which of the following must be true?
A. Δ𝐹𝑂𝑌 is an acute triangle
B. Δ FAT is a right triangle
̅̅̅̅ ≅ ̅̅̅̅
C. 𝐹𝑇
𝑌𝐴
̅̅̅̅
D. 𝑌𝑂 ≅ ̅̅̅̅
𝑂𝐴
15) PROM is a rhombus, find the lengths of ̅̅̅̅
𝐶𝑂and ̅̅̅̅̅
𝑀𝐶 . b)
Find m∠𝑂𝑃𝑅
P
R
36
4 2
C
60°
S
M
T
16) LIKE is a rhombus. Solve for x, y, z, and w.
y
L
I
O
17) MARG is a rectangle. Find …
24
A. 𝑚∠𝐴𝑀𝑆
M
A
(5z+ 27)°
B. SR
2x +8
V
70
C. SA
w°
K
6x – 12
(3z + 51)°
E
S
R
D. MV
18) JORG is a kite. If 𝑚∠𝑂 = 34° and 𝑚∠𝑅 = 3𝑥°
and 𝑚∠𝐽 = 𝑥°. Find the value of x and 𝑚∠𝑅.
R
G
19) LARY is an isosceles trapezoid.
R A. If LW = 8 and AY = 21, find the length
of ̅̅̅̅̅
𝑊𝑅 .
A
O
W
J
B. If 𝑚∠𝐿𝐴𝑅 =148°, find
𝑚∠𝐴𝐿𝑌& 𝑚∠𝐴𝑅𝑌.
L
Y
20) Given: PUMA is a parallelogram
Prove: ∆𝑃𝑈𝑀 ≅ ∆𝑀𝐴𝑃
P
U
T
A
M
Statement
1. PUMA is a rhombus
Reason
1.
2. ∠𝑈𝑃𝑀 ≅ ∠_______ and
∠𝐴𝑃𝑀 ≅ ∠_______
2.
̅̅̅̅ ≅ 𝑈𝑀
̅̅̅̅̅
3. 𝑃𝐴
3.
4. ∆𝑃𝑈𝑀 ≅ ∆𝑀𝐴𝑃
4.