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Geometry Semester 1 Model Problems (California Essential Standards) Short Answer
GE 1.0
1. List the undefined terms in Geometry.
2. Match each of the terms
with the corresponding
example
a. A theorem.
b. A conjecture.
c. An axiom (postulate).
d. An undefined term.
e. Inductive Reasoning.
f. Deductive Reasoning.
U. Every student in Mr. Smith’s class drew a quadrilateral, measured
the interior angles, and found the sum. They discovered that all of
their sums were the same and generalized this was true for every
quadrilateral.
V. Shelly used a piece of paper as a model of a plane and described it
in her notes.
W. Rueben found a property of rhombi, but does not know if it can be
proven to be true.
X. Yasmine noticed that all rectangles have opposite sides congruent
and then found a way to prove this was true.
Y. Rachel used a property of parallelograms to calculate the lengths of
the sides of a polygon on her homework.
Z. Andrew noticed that the relationship between corresponding
angles has not been proven, but is accepted as true and is used to
prove that other angle relationships are true.
GE 16.0
3. Given: AB . What is the first step in constructing the perpendicular
bisector to AB ?
a.
b.
c.
d.
4.
Draw a line segment connecting points E and F.
From point C, draw an arc that intersects the line at points A and B.
Draw a line segment connecting points A and B.
From points A and B, draw equal arcs that intersect at points E and F.
Darla is constructing an equilateral triangle. Which of the following could be her first step?
a.
c.
b.
d.
5.
Marsha is using a straightedge and
compass to do the construction shown.
Which statement best describes the construction
Martha is doing?
a. a line through P parallel to line l by constructing
two lines perpendicular to the same line
b. a line through P parallel to line l by copying an
angle
c. a line through P perpendicular to line l
d. a line through P congruent to line l
6.
Amina is bisecting an angle. Which of the construction diagrams shown below best represents
the beginning of Amina’s construction?
c.
a.
b.
d.
GE 7.0
7. In the diagram, lines l and m are parallel. What
relationship exists between angles A and B? What
postulate or theorem supports that relationship?
8. Lines l and m are shown in each diagram. In which diagram MUST lines l and m be parallel?
a.
b.
c.
d.
9. For the quadrilateral shown, what is the value of
x?
10. In the diagram, quadrilateral TRAP is a trapezoid in
which TP  RA . What is the value of x?
11. In the diagram shown, what is the value of x?
12. Quadrilateral ABCD is circumscribed by a circle, as shown in the
diagram to the right. What is the measure of ∠C?
GE 5.0
13.
Given: ABCD is a rhombus
Which theorem or postulate could be
used to prove that  AED ≅ AEB ?
and AC bisects DB .
Prove:  AED ≅ AEB
14. In the diagram,
∠A ≅ ∠D and ∠B ≅ ∠E .
What additional information would be
enough to prove that  ABC ≅ DEF ?
GE 4.0
15. If  LMN and  PQR have sides LM ≅ PQ and MN ≅ QR , which pair of angles would need
to be congruent to be sufficient to prove that  LMN ≅ PQR ?
21. In the diagram, ABC is a right
triangle.
What is the slope of BC ?
24. Use the proof to answer the
question below.
Given: AB ≅ BC ; D is the midpoint of AC
Prove:  ABD ≅CBD
STATEMENT
1. AB ≅ BC ; D is the midpoint 1. Given
of AC
REASON
2. AD ≅ CD
2. Definition of midpoint
3. BD ≅ BD
4.  ABD ≅CBD
4. ?
3. Reflexive Property
Which triangle equality theorem or postulate can be used as a
correct reason for step 4?
a.
25.
Given: ∠2 ≅ ∠3
Prove: ∠1 ≅ ∠4
Use the proof to answer the question below.
STATEMENT
1. ∠2 ≅ ∠3
2. ∠1 ≅ ∠2; ∠3 ≅ ∠4
3. ∠1 ≅ ∠4
REASON
1. Given
2. ?
3. Transitive Property
What reason can be used to justify step 2?
GS 13.0
33.
In the diagram shown, m∠CBD = 95˚. What is the
measure of ∠CDB ?
60.
The diagram shows a trapezoid with a height of 4 cm.
What is the area of the trapezoid?
34.
In the diagram shown, P is a point on ML . What is the
measure of the angle marked X?