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Geometry 6.1 - 6.3 Review
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Find 𝑚 ∠ 𝑋 𝑌 𝑍 m∠XYZ. In quadrilateral XYZW, two angles are given: 𝑚 ∠ 𝑊 𝑋 𝑌 = ( 7 𝑥 + 15 ) ∘ m∠WXY=(7x+15) ∘ 𝑚 ∠ 𝑌 𝑍 𝑊 = ( 5 𝑥 + 25 ) ∘ m∠YZW=(5x+25) ∘ Given that XYZW is a parallelogram, find 𝑚 ∠ 𝑋 𝑌 𝑍 m∠XYZ.
m∠XYZ=83.35 ∘
The vertices of PQRS are 𝑃 ( − 2 , 4 ) P(−2,4), 𝑄 ( 6 , 8 ) Q(6,8), 𝑅 ( 10 , − 2 ) R(10,−2), and 𝑆 ( 2 , − 6 ) S(2,−6). Determine the most precise classification of quadrilateral PQRS: parallelogram, rectangle, rhombus, or square.
Since 𝑃 𝑅 ≠ 𝑄 𝑆 PR  =QS, PQRS is a parallelogram, but not a rectangle or rhombus. Final Classification: Parallelogram Parallelogram
Find the equations of the diagonals for parallelogram ABCD in slope-intercept form. Given the vertices: 𝐴 ( 1 , 5 ) , 𝐵 ( 7 , 9 ) , 𝐶 ( 3 , − 1 ) , 𝐷 ( − 3 , − 5 ) A(1,5),B(7,9),C(3,−1),D(−3,−5) Find the equations of the diagonals 𝐴
Diagonal AC: y=−3x+8 Diagonal BD:  𝑦 = 7 5 𝑥 − 4 5 Diagonal BD: y= 5 7 ​ x− 5 4
If 𝑃 𝑄 = 50 PQ=50 and 𝑅 𝑆 = 18 RS=18, find 𝑃 𝑅 PR. In quadrilateral PQRS, diagonals intersect at point M. Given that 𝑃 𝑄 = 50 PQ=50 and 𝑅 𝑆 = 18 RS=18, use the properties of diagonals of a parallelogram to find 𝑃 𝑅 PR.
𝑃 𝑅 = 50 PR=50.
Find 𝑚 ∠ 𝐴 𝐵 𝐶 m∠ABC. In quadrilateral ABCD, two angles are given: 𝑚 ∠ 𝐵 𝐶 𝐷 = ( 5 𝑥 + 10 ) ∘ m∠BCD=(5x+10) ∘ 𝑚 ∠ 𝐷 𝐴 𝐵 = ( 3 𝑥 + 20 ) ∘ m∠DAB=(3x+20) ∘ Given that ABCD is a parallelogram, find 𝑚 ∠ 𝐴 𝐵 𝐶 m∠ABC.
𝑚 ∠ 𝐴 𝐵 𝐶 = 93.75 ∘ m∠ABC=93.75 ∘ .
The vertices of quadrilateral QRST are Q(2, 3), R(6, 7), S(10, -1), T(6, -5). Determine the most precise classification of QRST as a parallelogram, rectangle, rhombus, or square.
Parallelogram (most precise classification).
What is the equation of the diagonals for parallelogram ABCD in slope-intercept form? Given vertices: A(1, 5), B(7, 9), C(3, -1), D(-3, -5)
Diagonal AC: 𝑦 = − 3 𝑥 + 8 y=−3x+8 Diagonal BD: 𝑦 = 1.4 𝑥 − 0.8 y=1.4x−0.8
In the given parallelogram, find the measure of angle Y.
100 degrees
Find the measure of the indicated angle.
63 degrees
Find the length of RP.
39.6
In the given parallelogram, find the measure of angle R.
135 degrees
Can you prove the quadrilateral is a parallelogram using the given information? Explain.
No. Only one pair of opposite angles are congruent.
In the given parallelogram, solve for x.
x = 9
In the parallelogram KLMN, find the measure of angle N.
46 degrees
In the parallelogram DEFG, find the value of x.
x = 8
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