Download I can statements for proofs unit (2)

Geometry Test “I Can” Review
Name:______________________________ #
Work through the practice problems for each learning target on a separate sheet of paper. Check your answers after every two
or three statements.

I can read and understand an If-Then Statement.
1) Draw a diagram then write the hypothesis as the “Given” and the conclusion as the “Prove”.
If ∠𝑄𝑅𝑆 and ∠𝑆𝑅𝑇 are complementary angles, then 𝑚∠𝑄𝑅𝑆 + 𝑚∠𝑆𝑅𝑇 = 90°.
2) If ̅̅̅̅
𝐴𝐵 ⊥ ̅̅̅
𝐾𝐽 and ̅̅̅̅
𝐴𝐵 bisects ̅̅̅
𝐾𝐽,then ̅̅̅̅
𝐴𝐵 is the perpendicular bisector of ̅̅̅
𝐾𝐽.

I can classify adjacent angles, linear pairs, and vertical angles. I can use the properties of these angles to solve for
missing information. I can apply the Linear Pair Postulate and Angle Addition Postulate & the Segment Addition Postulate.
3) Use the picture on the right for the following:
a) Explain why ∠1 and ∠2 are not a linear pair.
b) Explain why ∠1 and ∠2 are not vertical angles.
c) Explain why ∠1 and ∠2 are not adjacent angles.
4) In the picture below, 𝑚∠1 = 47°. Find 𝑚∠2 and 𝑚∠3.
5) Complete each statement then state the postulate or theorem being used.
a)

b)
c)
I can use the addition and subtraction properties of equality and the reflexive, substitution, and transitive properties.
6) Identify the property demonstrated by each example.

a)
b)
̅̅̅̅ = 𝑚𝐿𝑀
̅̅̅̅, so 𝑚𝐸𝐹
̅̅̅̅ + 𝑚𝐹𝐿
̅̅̅̅ = 𝑚𝐹𝐿
̅̅̅̅ + 𝑚𝐿𝑀
̅̅̅̅
c) 𝑚𝐸𝐹
e)
̅̅̅̅ 𝑎𝑛𝑑 𝐿𝑀
̅̅̅̅ ≅ 𝑋𝑌
̅̅̅̅, 𝑠𝑜 ̅̅̅̅
̅̅̅̅
d) ̅̅̅̅
𝐴𝐵 ≅ 𝐿𝑀
𝐴𝐵 ≅ 𝑋𝑌
f)
I can prove theorems using a two-column proof.
7)

I can prove theorems by completing a flowchart proof or a paragraph proof.
9)
8) Prove this statement using a simple
paragraph proof.
Given: ∠1 and ∠2 form a linear pair.
Prove: ∠1 and ∠2 are supplementary.
 I can identify pairs of special angles formed by parallel lines cut by a transversal.
10)
Identify all angles congruent to ∠3 then explain how you
know (for example: the angles are corresponding,
alternate interior, etc..).
11) Identify all angles supplementary to ∠3 then explain
how you know.

I can determine if two triangles are congruent by HL, SSS, SAS, ASA or AAS.
12) Determine if you have enough information to declare the two triangles congruent. If you have enough information, explain
how you know then name the congruent triangles. If you do not have enough information, explain what is missing.
a)
b)
c)
d)
13) If you have proven two triangles are congruent by one of the congruence methods above, then CPCTC tells you that
corresponding parts are congruent in those triangles. Name the corresponding part for each of the following.
a)
b)
̅𝐼𝐻
̅̅̅ ≅ ?
Geometry Test “I Can” Review 2
Name:______________________________ #
Work through the practice problems for each learning target on a separate sheet of paper. Check your answers after every two
or three statements.
 I can prove triangles are congruent using triangle congruence theorems.
1)
2)
̅̅̅̅ and ̅̅̅̅
̅̅̅̅ ≅ 𝑆𝑅
Given 𝑃𝑇
𝑃𝑄 ≅ ̅̅̅̅
𝑄𝑅
Prove: ∆𝑇𝑃𝑄 ≅ ∆𝑆𝑅𝑄

I can apply the properties of parallelograms and other quadrilaterals. I can use what I’ve learned about lines, angles &
triangles to prove quadrilaterals are parallelograms.
3) STUV is a parallelogram. Solve for x.
4) STUV is a parallelogram
5)
6)
7) Given URST is a kite. Prove ̅̅̅̅
𝑇𝑉 ≅ ̅̅̅̅
𝑅𝑉 .
Provide the reasons for each statement of the proof to the
left using the figure below.
 I can apply the properties of the circumcenter of a triangle.
8) Lee’s job requires him to travel to downtown Raleigh, downtown Durham, and downtown Chapel Hill daily. The distance
from Raleigh to Durham is 26 miles. The distance from Durham to Chapel Hill is 14.2 miles. The distance from Chapel Hill to
Raleigh is 29.1 miles. Although it is not a perfect right triangle, it is very close. Draw and label a sketch to show where Lee
should buy a home so that he is equal distance from each place. Use your sketch to estimate the distance the home would be
from each city.
 I can apply the properties of the incenter of a triangle.
9)
A city plans to build a firefighters’ monument in the park between
three streets. The perpendicular distance from the monument to
Callahan Street is 24.75 feet. The distance from this point
intersection to the corner of Market and Callahan is 112 feet. If a
pedestrian stands at the corner of Callahan and Market, how far
would they be from the monument?

Callahan Street
Market Street
I can apply the properties of the centroid of a triangle.
10)
Marco is trying out a new design for a corner table. He has decided to put
one large post at the centroid of his triangular table. He measures the
distance from point G to point MB.
a) According to his measurements, it is 16 inches from G to MB.
If Marco has measured correctly, how far is it from G to B?
b) The area of ⊿𝐴𝐺𝑀𝐵 is 160 in2. What is the area of the entire top of
the table?

I can use the formulas for the volume of a Cylinder, Cone, Pyramid, Prism and Sphere.
11) Find the volume of the pyramid to the left.
12) Suppose a cone was constructed around the pyramid in such a way
that the base of the pyramid was inscribed in the base of the cone and the
cone had a height of 4.5 mi. Find the volume of the cone.

I can compare volumes of the same shape with different dimensions to determine which dimension has a greater effect
on the volume.
13) Which is a better deal? A can of baked beans with a diameter of 10 cm and a height of 10 cm for $3.19 or a can of baked
beans with a diameter of 8 cm and a height of 14 cm for $2.89? Explain.

I can use multiple volume formulas together to find the volume of composite shapes.
14) Ms. Pace had a special dog house built for her dog,
Franklin. Find the volume (living area) of this house if the
diameter of the base is 6 feet and the total height is 8 feet.
The distance from the floor to the lowest part of the roof is
5.75 feet.