1. Geometry Topic 2 & 3 Exam Review – Part 2 of 2
Mr. Urrusuno
Geometry Topic 2 & 3 Exam Review – Part 2 of 2

2. 1.) Know how to construct a square inside a circle…

7. 1.) Karenis reads the statement below in a geometry textbook:
“Construct the diameter of the circle and label the endpoints P and Q. Set the compass to be wider than the radius of the circle and construct a perpendicular bisector of segment PQ.” Which construction is best described by this statement?
A.) isosceles triangle
B.) equilateral triangle
C.) a regular hexagon inscribed in a circle
D.) a square inscribed in a circle
Correct answer:

8. 2.) Kevin drew triangle ABC then reflected it over line m to create triangle WXY.
Kevin concludes that the triangles are congruent. Which is a correct validation for this conclusion?
A.) When the triangle was reflected, the base of the resulting triangle lies on the same line as the base of the original triangle.
B. )When the triangle was reflected, the corresponding sides of the resulting triangle have slopes that are opposite to the slopes of the original triangle.
C.) When the triangle was reflected, the height of the resulting triangle is parallel to the height of the original triangle.
D. )When the triangle was reflected, the corresponding sides and angle measures of the resulting triangle are the same as the original triangle. 
Correct Answer:
D.) When the triangle was reflected, the corresponding sides and angle measures of the resulting triangle are the same as the original triangle. 

9. 3.) What is the equation of the line that is perpendicular to the line 𝑦=− 1 4 (𝑥 −20) and intersects the y-axis at 0, −2 ?
A.) 𝑦=4𝑥 −2
B.) 𝑦=−4𝑥 −2
C.) 𝑦=− 1 4 𝑥 −2
D.) 𝑦= 1 4 𝑥 −2
Correct answer:

10. Explanation for #3:
𝑦=− 1 4 𝑥 −20 Distributive property → 𝑦=− 1 4 𝑥 𝑦 = − 1 4 𝑥 + 5 Perpendicular line → 𝑦 = 4𝑥 +𝑏 To find “b”, substitute 0, −2 𝑓𝑜𝑟 𝑥 𝑎𝑛𝑑 𝑦… −2= 4 0 +𝑏 −2 = 𝑏 Final answer in slope-intercept form: 𝑦= 4𝑥 −2

11. 4.) Steps for Constructing a hexagon inscribed in a circle…
𝑻𝒉𝒊𝒔 𝒊𝒔 𝒕𝒉𝒆 𝒌𝒆𝒚 𝒔𝒕𝒆𝒑!
Step 2:
Step 5:
Step 3:

12. Which of these would be the next step of construction?
4.) Jordan wants to construct a regular hexagon inscribed in a circle with center A and diameter BC.
Which of these would be the next step of construction?
A.) Place the compass at A and draw an arc of length AB across the circle.
B.) Place the compass at B and draw an arc of length BC across the circle.
C.) Place the compass at C and draw an arc of length CB across the circle.
D.) Place the compass at B and draw an arc of length AB across the circle.
Correct answer: B A C

13. 5.) In the figure below, ∆ 𝑀𝑁𝑂 ≅∆PQR.
What is the measure of <𝑃 ?
A.) 9.8°
B.) 15.6 °
C.) 25.4 °
D.) 29.8 °
Correct answer:
(x = 9.8 then substitute it for x to find the m<P: 2(9.8) = 29.8 °).

14. 6.) Triangle ABC is an isosceles triangle, where <A is the vertex angle, m<A = 70°, and m<C = (5𝑥+12)°.
What is the value of x?
A.) 2.3
B.) 8.6
C.) 4.7
D.) 3.5
Correct answer:

15. Explanation for #6:
If triangle ABC is an isosceles triangle, and <A is the vertex angle, that means that <B and <C are the two base angles which are equal to each other. Therefore…
70° + 2(5x + 12)° = 180°
70+10𝑥+24 =180
10𝑥+94=180
10𝑥=86
𝑥 =
𝑥 = 8.6

16. 7.)
Be familiar with the steps for constructing a parallel line that goes through a point. →

17. 7.) Be prepared to arrange the steps in the correct order to show the construction of the line passing through point R that is parallel to 𝑃𝑄 .
Steps 1 through 4: Steps 5 through 7:

18. 8.) What is the equation of a line parallel to 5𝑥+2=𝑦 and passing through (6, −3) ?
B.) 5𝑥 −13=𝑦
C.) − 1 5 𝑥 + 2=𝑦
D.) − 1 5 𝑥 −13=𝑦
Correct Answer:

19. Explanation for #8:
5𝑥+2=𝑦 is already in slope-intercept form, they just put the y on the right side instead of the usual left side. Two parallel lines will always have the same slope. In this case, the slope is 5. Since the line is passing through the point 6, −3 , substitute those values for x and y to solve for the y-intercept, b. 5𝑥+𝑏=𝑦 5 6 +𝑏=−3 30+𝑏=−3 𝑏=−3 −30 𝑏=−33 𝐹𝑖𝑛𝑎𝑙 𝐴𝑛𝑠𝑤𝑒𝑟: 5𝑥 −33=𝑦

20. 9.) Segment BD is a midsegment of triangle AEC.
Which equation could be used to
find the value of x?
A.) 2(9𝑥 −11)=2(7𝑥+6)
B.) 2(9𝑥 −11)=7𝑥+6
C.) 9𝑥 −11=2(7𝑥+6)
D.) 9𝑥 −11=7𝑥+6
Correct Answer:

21. 10.) In the figure below, ∆PQR is a reflection of ∆ TSR.
Two students describe the given triangles as shown:
Student 1: Because reflections preserve side lengths, 𝑄𝑅 ≅ 𝑆𝑅 ,
𝑃𝑄 ≅ 𝑇𝑆 , 𝑎𝑛𝑑 𝑃𝑅 ≅ 𝑇𝑅 , 𝑠𝑜 ∆𝑃𝑄𝑅≅∆𝑇𝑆𝑅 𝑏𝑦 𝑆𝑆𝑆.
Student 2: Because reflections preserve both side lengths and angle measures,
<RQP≅<𝑅𝑆𝑇, 𝑄𝑅 ≅ 𝑆𝑅 , 𝑃𝑄 ≅ 𝑇𝑆 , 𝑠𝑜 ∆𝑃𝑄𝑅≅∆𝑇𝑆𝑅 𝑏𝑦 𝑆𝐴𝑆.
Which student has proven ∆𝑃𝑄𝑅≅∆𝑇𝑆𝑅 correctly?
Correct Answer:
Both student 1 and student 2

22. 11.) A square is being constructed inside of a circle with center A.
Point B will serve as one of the vertices of the square.
Determine whether the methods listed below will
help to find any of the other 3 vertices.
Correct answer: A B
Will help.
Will not help.
Construct a perpendicular line through 𝐵𝐴 that intersects the circle in two spots. ✓
Set the compass to the length of the circle’s radius. With the point of the compass set at B, strike two marks that intersect the circle.
Draw a line through 𝐵𝐴 that intersects the circle.

23. Determine whether each statement is true or false.
12.)In the diagram below, quadrilateral ABDC is a rectangle. Diagonal 𝐴𝐷 splits the rectangle into triangles ABD and DCA.
Determine whether each statement is true or false.
True
False
Triangles ABD and DCA are congruent because there is a rotation that carries one triangle onto the other. ✓
Triangles ABD and DCA are congruent because there is a translation that carries one triangle onto the other.
Triangles ABD and DCA are congruent because of SSS.
Triangles ABD and DCA are congruent because of SAS.

24. 13. ) Juan wants to prove the Base Angles Theorem
13.) Juan wants to prove the Base Angles Theorem. His two-column proof is shown below.
Statements
Reasons
𝐴𝐵 ≅ 𝐵𝐶
Given
𝐷𝐵 bisects <ABC
<ABD ≅ <CBD ?
𝐵𝐷 ≅ 𝐵𝐷
∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷
<A ≅ <C B A D C
Given: 𝐴𝐵 ≅ 𝐵𝐶 ; 𝐷𝐵 bisects <ABC
Prove: <A ≅ <C
Correct Answer:

25. 14.) For Mr. Urrusuno’s student’s:
Mr. U will give you the answer to the question with this picture.