Download 1. The measures of two vertical angles are (10x – 24)° and 2x

Geometry Mini Midterm
Name: _________________________________
1. The measures of two vertical angles are (10x – 24)° and 2x°. Find x.
2. Find the values of x and y so that ∆ABC ≅ ∆DEF by HL
A
D
4x -6
B
8x - 30
8
C
3y - 19
F
E
3. Write the following formulas:
A. Midpoint
B. Distance
C. Slope
4. A postulate is
5. Match each.
____ Orthocenter
A. The point of concurrency of the three medians of a triangle.
____ Incenter
B. The point of concurrency of the three ⊥ bisectors of a triangle.
____ Circumcenter
C. The point of concurrency of the three ∠ bisectors of a triangle.
____ Centroid
D. The point of concurrency of the three altitudes.
Determine the correct answer for each.
6. Where do the 3 medians of a triangle intersect?
A) inside the triangle B) Outside the triangle
C) On the triangle
D) Any of these
7. Where do the 3 altitudes of a triangle intersect?
A) inside the triangle B) Outside the triangle
C) On the triangle
D) Any of these
R
8. Find the longest side of PQRS.
45°
Q
50°
55°
65°
S
P
R
9.
Given: RF ⊥ AT
F is a midpoint of AT
Prove: ∠ARF ≅ ∠TRF
A
Statements
F
Reasons
1. RF ⊥ AT
1. Given
2. ∠AFR and ∠TFR are right angles
2.
3. ∠AFR ≅ ∠ TFR
3.
4. RF ≅ RF
4.
5.
5. Given
6.
6. Definition of Midpoint
7. ∆AFR ≅ ∆TFR
7.
8. ∠ARF ≅ ∠TRF
8.
T
Geometry Mini Midterm
Name: _________________________________
1. The measures of two vertical angles are (10x – 24)° and 2x°. Find x.
10x – 24 = 2x
− 24 = −8x
3= x
2. Find the values of x and y so that ∆ABC ≅ ∆DEF by HL
A
4x -6
8x - 30
8
B
4x−6 = 8x−30
4x + 24 = 8x
24 = 4x
6=x
D
C
3y - 19
F
8 = 3y-19
27 = 3y
9=y
E
3. Write the following formulas:
A. Midpoint
B. Distance
 x + x 2 y1 + y 2 
M= 1
,

2 
 2
4. A postulate is
d=
( x 2 − x1 )
C. Slope
2
+ ( y 2 − y1 )
2
m=
y 2 − y1
x 2 − x1
a rule that is accepted without proof.
5. Match each.
D Orthocenter
A. The point of concurrency of the three medians of a triangle.
C
Incenter
B. The point of concurrency of the three ⊥ bisectors of a triangle.
B Circumcenter
C. The point of concurrency of the three ∠ bisectors of a triangle.
A Centroid
D. The point of concurrency of the three altitudes.
Determine the correct answer for each.
6. Where do the 3 medians of a triangle intersect?
A) inside the triangle B) Outside the triangle
C) On the triangle
D) Any of these
7. Where do the 3 altitudes of a triangle intersect?
A) inside the triangle B) Outside the triangle
C) On the triangle
D) Any of these
R
8. Find the longest side of PQRS.
First, find the two missing angles
45°
Q
Be careful!
PR is not a side of
PQRS, so don’t
think it can be the
longest side!
60°
50°
The longest side is across the largest angle (85°) QR.
85°
65°
55°
S
P
R
9. Given:
Prove:
RF ⊥ AT
F is a midpoint of AT
∠ARF ≅ ∠TRF
A
Statements
1. RF ⊥ AT
2. ∠AFR and ∠TFR are right angles
3. ∠AFR ≅ ∠ TFR
4. RF ≅ RF
5. F is a midpoint of AT
6. AF ≅ FT
7. ∆AFR ≅ ∆TFR
8. ∠ARF ≅ ∠TRF
F
T
Reasons
1. Given
2. Def. Of Perpendicular Lines
3. All right angles are congruent
4. Reflexive Property of Segment Congruence
5. Given
6. Definition of Midpoint
7. SAS
8. Corresponding Parts of ≅ Triangles
are ≅ (CPCTC)