3.14.4 Test (TST) - Shapes (Test)
3.14.4 Test (TST) - Shapes (Test)
3.14.4 Test (TST) - Shapes (Test)
4
Test (TST): Triangles Test
Geometry Name:
Date:
Answer the following questions using what you've learned from this unit. Write your
answers in the space provided. Be sure to show all work.
Part I: Find the missing angle measure in each triangle. Show your work.
(3 points, 1 point each)
Part II: Use the measures from Part I to classify each triangle as acute, obtuse, or
right. Explain each classification. (3 points, 1 point each)
Part II: Can the three segments below form a triangle? Explain your answer.
(2 points)
AB = AB = AB =
BC = BC = BC =
AC = AC = AC =
CONGRUENT TRIANGLES
Part I: Draw the two congruent triangles described in the box. Label their vertices and
side lengths. (2 points)
AB = 6, GF = 8, AC = 10.
a. BC = b. EF = c. EG =
PROVE CONGRUENCE
a. SSS:
b. SAS:
c. ASA:
d. AAS:
Part II: In the triangles below, DF MN, DG MP, D P. Can you prove that
DFG MNP? Explain your answer. (2 points)
Given: AB DB and EB CB
Prove: D A.
Statements Reasons
1.
1.
2. ABC DBE 2.
3. 3. Side-angle-side postulate
SIMILAR TRIANGLES
Part I: In the diagrams below, ABC is similar to RST. Use a proportion with sides
AB and RS to find the scale factor of ABC to RST. Show your work. (2 points)
Part II: Use the scale factor from Part I and a proportion to find the length of ST.
Show your work. (1 point)
Part III: Use the scale factor from Part I and a proportion to find the length of RT.
Show your work. (2 points)
7. Fill in the missing statements and reasons in the proof. (4 points; 1 point each)
Given:
Prove: XY ZY
Statements Reasons
1. 1. Given
2. XW ZW 2.
4. YW YW 4.
5. WXY WZY 5.
6. XY ZY 6.
8. The tubes on the frame of this road bike form a triangle. The owner's manual
identifies some of the angle measures formed by the bike frame. Based on the
Part I: Classify the triangle formed by the three bike frame tubes as equilateral,
isosceles, or scalene. Find the measure of ∠B and explain your classification. (3
points; 1 point for classification, 1 point for the angle measure, and 1 point for
explanation)
Part II: List the three tubes — top, seat, and down tube — in order from shortest to
longest. Explain your reasoning. (4 points; 1 point for list, 3 points for
explanation)
1. _______________ (shortest)
2. _______________
3. _______________ (longest)
Step 1: Every proof needs Given and Prove statements. Use the endpoints on
the diagram to write a Given statement indicating the down tube is longer than
the top tube. Prove the relationship between the opposite angles of the given
sides. (2 points; 1 point for the Given statement, 1 point for the Prove
statement)
Given:
Prove:
Step 2: Use the spaces below to complete the formal proof. (7 points)
1. Given
4. m∠1 = m∠2
6. Substitution
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