Download midterm review - Brandywine School District

MIDTERM REVIEW
1. Two homes are built on a plot of land shown below. Both homeowners have dogs are
interested in putting up as much fencing as possible between their homes on the land
but in a way that keeps the fence equidistant from each home. Use your compass and
straightedge to determine where the fence should go on the plot of land. (3 pts)
House 1
House 2
2. The city of Springfield wants to build a new baseball stadium for their minor league
baseball team, the Isotopes. The planning committee would like the stadium to be
equidistant from two residential living areas. A sketch of the city appears below, with
the residential areas labeled as R1 and R2. Identify two possible locations for the
stadium, and label them S1 and S2. Then clearly and precisely list the mathematical steps
used to determine each of the two possible locations. (8 pts)
Park
High School
R1
School
Mall
R2
Park
Corporate
Center
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
3. Use the diagram below to find the angle measures. Explain your reasoning.
a) If the 𝑚∠7 = 75°, what is the 𝑚∠3? (2 pts)
b) If the 𝑚∠4 = 111°, what is the 𝑚∠5? (2 pts)
4. Solve for the value of x in the diagram below. Then find the measures of the acute and obtuse
angles. (5 pts)
5. Find the values of x and y in the diagram below. Show all work. (5 pts)
x = _____________________
y = ____________________
6. Find the measures of b and c in the diagram below. Give the reasons for your solutions.
(4 pts)
b = _____________________
c = ____________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
7. Prove that exterior angle of a triangle is the sum of the two remote interior angles.
(4 pts)
Prove: 𝑚∠𝑥 + 𝑚∠𝑦 = 𝑚∠𝑧
8. Prove that vertical angles are congruent. You choose the vertical angles. (4 pts)
9. In the figure below, 𝐴𝐵 ∥ 𝐶𝐷 and 𝐵𝐶 ∥ 𝐸𝐷.
Prove that𝑚∠𝑏 + 𝑚∠𝑑 = 180°. (4 pts)
10. Reflect ABCD across 𝐸𝐹. (6 pts)
F
B
A
C
D
E
11. Translate Δ𝐴𝐵𝐶 across ⃑⃑⃑⃑⃑
𝐸𝐹 . (6 pts)
A
B
E
F
C
12. Locate the center of rotation below using constructions. Then identify the angle of
rotation. (6 pts)
13. Identify all the lines of symmetry and the rotational symmetries in the regular figure
below. (6 pts)
14. Precisely define each of the three rigid motion transformations below. (6 pts)
a. 𝑇̅̅̅̅
𝐴𝐵 (∆𝐴𝐵𝐶)
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
b. 𝑟𝑋𝑌
̅̅̅̅ (∆𝐷𝐸𝐹)
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
c. 𝑅𝐶,30° (∆𝐿𝑀𝑁)______________________________________________________
__________________________________________________________________
__________________________________________________________________
15. Complete the table based on the series of rigid motions performed on Δ𝐴𝐵𝐶 below.
(10 pts)
Sequence of Rigid Motions (2)
Composition in symbolic
notation
Sequence of Corresponding
Sides
Sequence of Corresponding
Angles
Triangle Congruence Statement
16. Given: ∆𝑅𝑆𝑇 is isosceles, SY = TZ.
Prove: ∆𝑅𝑆𝑌 ≅ ∆𝑅𝑇𝑍
17. Given: ∠𝐴𝐷𝐵 ≅ ∠𝐶𝐵𝐷, ∠𝐴𝐵𝐷 ≅ ∠𝐶𝐷𝐵
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
Prove: 𝐴𝐷
A
D
B
C
18. Review all Problem Set questions, examples and class exercises from the
Lessons we completed in marking periods 1 and 2.
19. The Constructions Review is linked off of Mr. Merkel’s website under Math
Resource. This will help you review your constructions.