Download Geometry Chapter 7 Post-Test Worksheet KEY Problem # Concept

Geometry
Chapter 7 Post-Test Worksheet KEY
Problem # Concept
Properties of Quadrilaterals: Verify, apply and prove
properties of quadrilaterals.
1-4
Mastered
Needs Retake
1. Prove the following using either a two column proof or a flow chart. Make sure to include all of your reasons
to support your statements.
H
M
Given:
K is the midpoint of ̅̅̅̅
𝐽𝑀 and𝐻𝐽𝐾  𝐿𝑀𝐾
Prove:
̅̅̅̅ ≅ 𝐿𝑀
̅̅̅̅
𝐻𝐽
J
K
L
STATEMENT
1) K is the midpoint of ̅̅̅̅
𝑱𝑴
2) JK = MK
3) ∠𝑯𝑱𝑲 ∠𝑳𝑴𝑲 ≅
4) ∠𝑯𝑲𝑱 ≅ ∠𝑳𝑲𝑴
5) ∆𝑯𝑲𝑱 ≅ ∆𝑳𝑲𝑴
̅̅̅̅ ≅ ̅̅̅̅̅
6) 𝑯𝑱
𝑳𝑴
JUSTIFICATION
1) Given
2) Definition of midpoint
3) Given
4) Vertical Angles are ≅
5) ASA ≅
6) ≅ ∆𝐬 ⟶≅ 𝐩𝐚𝐫𝐭𝐬
2. Prove that if a pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral must
̅̅̅̅ ∥ 𝐶𝐷
̅̅̅̅ and 𝐴𝐵
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅ , prove
be a parallelogram. For example, for the quadrilateral ABCD shown, given that 𝐴𝐵
̅̅̅̅
̅̅̅̅
that 𝐵𝐶 ∥ 𝐴𝐷 . Organize your reasoning in the two column proof.
B
A
1. ̅̅̅̅
𝑨𝑩 ∥ ̅̅̅̅
𝑫𝑪
1. Given
2. ∠𝑨𝑪𝑫 ≅ ∠𝑪𝑨𝑩
2. Alternate Interior Angles
̅̅̅̅  𝐶𝐷
̅̅̅̅
3. 𝐴𝐵
3. Given
4. ̅̅̅̅
𝑨𝑪 ≅ ̅̅̅̅
𝑨𝑪
4. Reflexive Property
5. ∆ABC  ∆CDA
5. SAS ≅
6. ∠𝑨𝑪𝑩 ≅ ∠𝑪𝑨𝑫
6. ≅ ∆s ⟶≅ parts
̅̅̅̅ ∥ ̅̅̅̅
7. 𝐵𝐶
𝐴𝐷
7. AIA ≅⟶∥ 𝐋𝐢𝐧𝐞𝐬
C
D
Geometry
Chapter 7 Post-Test Worksheet KEY
3. Fill-in the blank with the Definition of each Quadrilateral. (Hint: use your glossary.)
A) Rhombus: quadrilateral with 4 congruent sides.
B) Square: quadrilateral with 4 right angles and 4 congruent sides.
C) Parallelogram: quadrilateral with 2 pairs of parallel sides.
D) Kite: quadrilateral with 2 distinct pairs of consecutive congruent sides.
E) Trapezoid: quadrilateral with at least one pair of parallel sides.
S
4. In the figure at right, SL = 48cm and SI= 16cm.
a. State why SMI ~ SLE . Be specific and make your
explanation complete.
M
I
L
E
[Angle S is congruent to itself by the identity property. The ratios of sides SM/SL and SI/SE are both ½.
Therefore by SAS ~, ∆SMI ~ ∆SLE.]
b. Find all side lengths of SMI and SLE . SHOW ALL WORK.
SM = 24cm, SE = 32cm, MI ≈ 28.84cm, LE ≈ 57.69cm
c. Is MI // LE ? Justify your conclusion.
[Yes. ∠𝑺𝑴𝑰 ≅ ∠𝑺𝑳𝑬 (𝐬𝐢𝐦𝐢𝐥𝐚𝐫 𝐭𝐫𝐢𝐚𝐧𝐠𝐥𝐞𝐬 𝐡𝐚𝐯𝐞 ≅ 𝐚𝐧𝐠𝐥𝐞𝐬), 𝒔𝒐 ̅̅̅̅
𝑴𝑰 ∥ ̅̅̅̅
𝑳𝑬 𝐛𝐞𝐜𝐚𝐮𝐬𝐞 if corresponding angles
are congruent, then lines are parallel.]
Geometry
Chapter 7 Post-Test Worksheet KEY
Problem # Concept
Midpoint, Distance and Slope: Use midpoint, distance and
slope properties to determine relationships between line
1-4
segments.
Mastered
Needs Retake
1. For the segment with endpoints A(1, 6) and B(3, 8)
a. Find the midpoint of line segment ̅̅̅̅
𝐴𝐵 .
[(2, 7)]
̅̅̅̅.
b. Find the length of line segment 𝐴𝐵
[≈ 2.83 units]
̅̅̅̅ name the coordinates of point C.
c. If point A is the midpoint of 𝐵𝐶
[C(-1, 4)]
2. Plot the points A (0, 0), B (8,0), C (8,6), D (2,6). What shape is ABCD (name it completely)? Use the
length & slope of each side to justify your conclusion. Show All Work
̅̅̅̅ 𝒊𝒔 𝒛𝒆𝒓𝒐 & 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑩𝑪
̅̅̅̅ 𝒊𝒔 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆𝒅, 𝒔𝒐 𝑩𝑪
̅̅̅̅ ⊥
̅̅̅̅ 𝒂𝒏𝒅 𝑪𝑫
[𝒔𝒍𝒐𝒑𝒆 𝒐𝒇 𝑨𝑩
̅̅̅̅
̅̅̅̅
̅̅̅̅
𝑨𝑩 𝒂𝒏𝒅 𝑪𝑫. 𝑻𝒉𝒆 𝒔𝒍𝒐𝒑𝒆 𝒐𝒇 𝑫𝑨 𝒊𝒔 𝟑, so its angles are not 90°. ABCD is a right trapezoid b/c it has 2
right angles and 1 pair of parallel sides.]
Geometry
Chapter 7 Post-Test Worksheet KEY
3. Find the midpoint of segment ̅̅̅̅
𝐴𝐵 , if A(-4, 9) and B(-13, -18)
[(-8.5, -4.5)]
4. Plot and connect the points
S (0, 0) T (0, 5), A (4, 6), R (7, 2)
to form quadrilateral STAR.
What shape is STAR? Use the slope of the sides
to justify your answer completely.
[quadrilateral: no slopes are congruent or opp. inverse, so
no parallel or perpendicular sides.]