Download Geometry Module 6 Check for Understanding

Geometry Module 6 Check for Understanding
____
1. Given: diagram showing the steps in the construction
Prove:
is the perpendicular bisector of
A
P
R
Q
B
Complete the proof.
Proof:
Statements
Reasons
.
1. [1]
2. Same compass setting used
3. Reflexive Property of Congruence
4. [2]
4. SSS
5. CPCTC
6. SAS
7. CPCTC
.
8. Definition of midpoint
9. [3]
10. Definition of perpendicular bisector
A [1] Through any two points there is exactly one line.
[2]
[3]
B [1] Through any two points there is exactly one line.
[2]
[3]
C [1] Through any two points there is exactly one line.
[2].
[3]
D [1] Ruler Postulate
[2]
[3]
2. Consider the figure shown here.
.
.
.
.
A
n
a. Construct a line perpendicular to line that passes through point . Label your drawing
appropriately.
b. Suppose point lies on line . Are the steps you used in your construction from part a still valid?
Explain.
____
3. Tyler is using a compass and straightedge to inscribe an equilateral triangle inside circle O. His first step is to
draw diameter
. Describe Tyler’s next step in the construction.
P
Q
O
A Draw two more diameters that divide the circle into six equal pieces.
B Open the compass to a width of PQ, put the compass point on P (or Q), and draw an arc
that intersects the circle.
C Open the compass to a width greater than OQ, place the compass point at P and draw an
arc. Then place the compass point at Q and draw an arc. Then use the intersections of the
two arcs to draw a perpendicular bisector of
.
D Open the compass to a width of OQ, put the compass point on P (or Q), and draw an arc
that intersects the circle.
4. Use a compass and straightedge to inscribe a regular hexagon in a circle O. Label all vertices of the hexagon.
Leave all your construction marks.
5. Inscribe a square in the circle below.
O
____
6. The figure shows the paths through a park. Which justifies the statement
A SAS
B SSS
____
?
C ASA
D HL
7. What additional information will prove
by HL?
A
B
____
8. A jogging path runs along the river from point
to point , passing through point . You want to find the
distance
across a river using indirect measurement. Which congruence criterion can be used to show that
?
D
C
100 ft
A
100 ft
B
E
A
B
C
D
SSS
ASA
SAS
HL
9.
If
and
10. In the diagram,
are right angles and
. Explain why
, what postulate or theorem proves
.
?
Geometry Module 6 Check for Understanding
Answer Section
1. ANS: A
PTS: 1
DIF: DOK 3
OBJ: Proving the Construction of a Midpoint
STA: G-CO.12
TOP: Proving Constructions Valid
2. ANS:
a. Names for new points may vary.
NAT: G-CO.D.12
KEY: proof | construction
m
A
X
Y
n
b. Yes, this construction is valid if point lies on line . Regardless of the position of point
always be drawn that intersects line in two points.
, an arc can
Rubric
a. 1 point for using an arc to locate and draw points
and ;
1 point for constructing the perpendicular bisector of
;
1 point for labeling line and marking perpendicular
b. 1 point for Yes; 1 point for valid explanation
PTS: 5
DIF: DOK 3
NAT: G-CO.D.12 | MP.5
STA: G-CO.12 | MP.5
KEY: construction | perpendicular line
3. ANS: D
PTS: 1
DIF: DOK 1
NAT: G-CO.D.13
STA: G-CO.13
KEY: drawing | inscribed | hexagon
4. ANS:
Answers may vary as there is no need for the radius (or diameter) to be shown as horizontal, but should
conform to one of the patterns shown. Paths shown in light gray need not be part of the answer--just the
intersections, shown in black.
C
B
O
D
C
A
B
D
A
O
E
F
E
F
or
PTS: 1
DIF: DOK 2
NAT: G-CO.D.13 STA: G-CO.13
KEY: compass-and-straightedge constructions | inscribed hexagon
5. ANS:
Possible answer:
C
A
O
B
D
Rubric
Point labels may vary.
1 point for drawing a diameter;
1 point for drawing arcs with centers and using the same radius;
1 point for drawing the perpendicular bisector of
through ;
1 point for drawing the correct segments to complete the square
PTS:
STA:
6. ANS:
STA:
7. ANS:
STA:
8. ANS:
4
DIF: DOK 2
NAT: G-CO.D.13 | MP.5
G-CO.13 | MP.5
KEY: construction | square | inscribed | circle
A
PTS: 1
DIF: DOK 1
NAT: G-SRT.B.5
G-SRT.5
B
PTS: 1
DIF: DOK 2
NAT: G-CO.C.10 | G-SRT.B.5
G-CO.10 | G-SRT.5
B
because they are vertical angles. Therefore,
by ASA.
Feedback
A
B
C
D
Only one side length is given in each triangle.
That’s correct!
Only one side length is given in each triangle.
The lengths of the hypotenuses are not given.
PTS: 1
DIF: DOK 1
NAT: G-SRT.B.5 STA: G-SRT.5
KEY: right triangles | vertical angles | congruent triangles | ASA
9. ANS:
HL
PTS: 1
DIF: DOK 2
NAT: G-CO.C.10 | G-SRT.B.5
STA: G-CO.10 | G-SRT.5
10. ANS:
By HL Congruence,
. By CPCTC,
.
PTS: 1
DIF: DOK 3
NAT: G-SRT.B.5
TOP: Prove Triangles Congruent by SAS and HL
STA: G-SRT.5
KEY: HL congruence