Download Geometry Chapter 7 Post-Test Worksheet Problem # Concept

Geometry
Chapter 7 Post-Test Worksheet
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:
̅𝐻𝐽
̅̅̅ ≅ ̅̅̅̅
𝐿𝑀
J
K
L
2. Prove that if a pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral must
be a parallelogram. For example, for the quadrilateral ABCD shown, given that ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐶𝐷 and ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷, prove
̅̅̅̅
̅̅̅̅
that 𝐵𝐶 ∥ 𝐴𝐷 . Organize your reasoning in the two column proof.
B
A
1.
1. Given
2.
2. Alternate Interior Angles
3. ̅̅̅̅
𝐴𝐵  ̅̅̅̅
𝐶𝐷
3.
4.
4. Reflexive Property
5. ∆ABC  ∆CDA
5.
6.
6. ≅ ∆s ⟶≅ parts
̅̅̅̅ ∥ ̅̅̅̅
7. 𝐵𝐶
𝐴𝐷
7.
C
D
Geometry
Chapter 7 Post-Test Worksheet
3. Fill-in the blank with the Definition of each Quadrilateral. (Hint: use your glossary.)
A) Rhombus _____________________________________________________________________
B) Square _______________________________________________________________________
C) Parallelogram__________________________________________________________________
D) Kite __________________________________________________________________________
E) Trapezoid _____________________________________________________________________
S
4. In the figure at right, SL = 48cm and SI= 16cm.
M
a. State why SMI ~ SLE . Be specific and make your
explanation complete.
L
b. Find all side lengths of SMI and SLE . SHOW ALL WORK.
c. Is MI // LE ? Justify your conclusion.
I
E
Geometry
Chapter 7 Post-Test Worksheet
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 .
̅̅̅̅.
b. Find the length of line segment 𝐴𝐵
̅̅̅̅ name the coordinates of point C.
c. If point A is the midpoint of 𝐵𝐶
2. Plot the points A (0, 0), B (6, 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
Geometry
Chapter 7 Post-Test Worksheet
3. Find the midpoint of segment ̅̅̅̅
𝐴𝐵 , if A(-4, 9) and B(-13, -18)
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 slopes of the
sides to justify your answer completely.