Math project end of year 10th grade

1. By: Dancayra Rosario

2. Question 1 :
Which point is on the line 4y-2x=0
A) (-2, -1)
B) (-1,2)
C) (1.2)
D) (-1,-2)
Unit 1: Points, lines, planes
Answer: 1
4(-1)-2(-2)=0
-4+4=0

3. Question 2 :
If line segment AB is contained in plane
P, and line segment AB is perpendicular to
plane R which statement is true?
A) line segment AB is parallel to plane R
B) Plane P is parallel to plane R
C) Line segment AB is perpendicular to
plane P
D) Plane P is perpendicular to plane R
Unit 1: Points, lines, planes
Answer: D
Because Line segment AB is perpendicular to plane R and line segment AB is in plane
P

4. UNIT 2: TRIANGLES PROPERTY
Question 1:
ABC≅ XYZ
•All 3 sides are congruent
•ZX = CA (side)
•XY = AB (side)
•YZ = BC (side)
•The Side Side Side postulate, the
triangles are congruent.

5. UNIT 2: TRIANGLES PROPERTY
Question 2:
△ABC≅△XYZ Two sides and the included angle are congruent
 AC = ZX (side)
 ∠ACB = ∠XZY (angle)
 CB = ZY (side)
The Side Angle Side postulate, the triangles are congruent.

6. If AB ≅ CD, which statement could always be
proven?
1) AC ≅ DB
2) AE ≅ ED
3) AB ≅ BC
4) EC ≅ EA
In AED with ABCD shown in the diagram
below, EB and EC are drawn.
Question 1:
Answer: 1
AB = CD
AB+BC = CD+BC
AC = BD

7. Question 2:
In the diagram below of triangle PRT, Q is a point
on segment PR, S is a point on segment TR, segment
QS is drawn, and angle RPT is congruent to angle RSQ.
Which reason justifies the conclusion that
PRT ∼ SRQ?
1) AA
2) ASA
3) SAS
4) SSS
Answer: 1 because there are only 2 angles
and no sides

8. Unit 4:Quadrilaterals
Question 1:
The opposite sides of a parallelogram are
represented by
2x + 10 and 5x - 20.
Find the length of the side of the parallelogram
represented by 4x - 1.
Work:
5x-20=2x+10
+20 +20 4(10)-1
5x=2x+30 40-1
-2x -2x length= 39
3x=30
3
X=10
The answer is 39 because
since the quadrilateral is a
rectangle there are 2 pairs of
congruent sides so I set the top
and bottom to equal each other
to get X and plugged it in to the
side that we had to solve.

9. Unit 4:Quadrilaterals
Question 2:
Which statement describe the properties of a trapezoid?
a. The bases are parallel.
b. The diagonals are congruent.
c. The opposite angles are congruent.
d. The base angles are congruent.
 Answer: A
 The answer is A because
the bases of a trapezoid
are parallel the diagonals
are not congruent

10. UNIT 5: TRANSFORMATION
 Question 1:
In the diagram shown triangle ABC is plotted
on the graph triangle ABC’ is also plotted after the
translation of (-5,6) what will the coordinates of
triangle ABC’’ after a rotation of 180 degree?
Answer:
A’’ (-4,1)
B’’(-4.3)
C’’(-1,3)
These are the answers because when
you do a rotation of 180 coordinates
(A.B) turns into coordinates (-A,-B)

11. UNIT 5: TRANSFORMATION
 Question 2:
What are the coordinates of
trapezoid ABCD after a
translation of (-2,-3)?
C’ D’
A’ B’
C
D
A B
A(2,1) A’(-1,1)
B(4,1) B’(1,-1)
C(1,4) C’(-2,2)
D(5,4) D’(2.2)
In order to find The coordinates of the
of the trapezoid after the translation
you needed to subtract 2 from the rise
of each point and subtract 3 from the
run of each point.

12. UNIT 6:CIRCLES Question 1:
 Find the value of x.
 Segment AB is a tangent
 Solution: x is a radius of the circle.
 Since x contains B, and AB
 is a tangent segment, x must be
 perpendicular to AB (the definition of
 a tangent tells us that).
 If it is perpendicular, the triangle
 formed by x, AB, and CA is a right
 triangle.

 Use the Pythagorean theorem to
 solve for x.

 152 + x2 = 172
 x2 = 64
 x = 8

13. UNIT 6:CIRCLES
Question 2:
In the accompanying diagram of
circle O, m<ABC= 2x and measure arc AC= x+60
Find the value of x.
Work:
2(2X)=X+60
4X=X+60
-X -X
3X=60
3
X=20
In order to find X you have to set <ABC times 2 and put it equal to X+60 and
solve it

14. UNIT 7: SURFACE AREA AND
VOLUME
 Question 1:
The rectangular prism shown below has a length
of 3.0 cm, a width of 2.2 cm, and a height of 7.5 cm
2.2
cm
3 cm 7.5cm
What is the surface area, in square
centimeters?
1) 45.6
2) 49.5
3) 78.0
4) 91.2
Answer: 4
SA = 2lw+2hw+2lh
SA= 2(3)(2.2)+2(7.5)(2.2)+2(3)(7.5) = 91.2
The answer is 4 because
you had to substitute the
length width and height
in order to find the
answer

15. UNIT 7: SURFACE AREA AND
VOLUME
 Question 1:
Find the volume, in cubic, of the rectangular prism
shown below.
 Answer:
V = lwh
10⋅2⋅4 =80
10 cm
4cm
2 cm
Finding the answer for this
problem is easy as long that
you know the formula which
is length times width times
height you substitue it and
you get the pruduct

16. EXTRA CREDIT!!!!
2 Locus problems
1 Translation problem
Angle triangle properties

17. LOCUS
A B
26 MILES
Point A and point B are 26 miles apart. How many points are 20 miles from
point A and 22 miles from point B?
Answer:
2 points
There are 2 points from 20 miles from A
to 22 miles from B because the 2 circles
intersect at only 2

18. LOCUS
Plot all the points 3 units
away from the orgin and plot
the points 2 units away from
The line X=1, state the
Coordinates and the amount
Of points of the locus’s.
3 points
(-1,-3)
(-1,3)
(3,0)

19. What is the image of the point under
the translation ?
A) (-9,5)
B) (-8,6)
C) (-2,-2)
D) (-15,-8)
Translation (extra)
Answer:
C (-2,-2)
-5+3=-2 2+-4=-2

20. Find the measure of angle C.
M<A=120
M<B=34
M<A + M<B + M<C = 180
120+34+M<C=180
154+M<C=180
M<C=26
Angle Properties of Triangles
Answer:
M<C=26
The answer is 26 because since a
whole triangle is 180 degrees
and there are 2 angles that have
a measure which is m<A=120
and m<B=34 so that means that
120+34 equals 154 and 180-154
equals 26