WorksheetsMU Gemetry Sem A Final Review
Total questions: 100
Worksheet time: 2hrs 48mins
Classify the triangle by its sides and by measuring its angles. The triangle can be classified by its angles as (a) and by its sides as (b) .
Classify △ABC by its sides. A(−2, 3), B(3, 4), C(1, −1)
Isosceles
Scalene
Equilateral
Is △ABC a right triangle? A(−2, 3), B(3, 4), C(1, −1)
Yes
No
Classify △ABC by its sides. A(2, 3), B(6, 3), C(2, 7)
Isosceles
Scalene
Equilateral
Is △ABC a right triangle? A(2, 3), B(6, 3), C(2, 7)
Yes
No
Find the measure of the exterior angle.
132
90
120
150
Find the measure of the exterior angle.
Find the measure of each acute angle.
The measure of the smaller angle is (a) , while the measure of the larger angle is (b) .
Find the measure of each acute angle.
The measure of the smaller angle is (a) , while the measure of the larger angle is (b)
In a right triangle, the measure of one acute angle is 4 times the difference of the measure of the other acute angle and 5. Find the measure of each acute angle in the triangle.
22 & 68
30 & 60
25 & 65
15 & 75
In the diagram, GHJK ≅ LMNP. Identify all pairs of congruent corresponding angles.
∠L
∠G
∠M
∠H
∠N
∠J
∠P
∠K
In the diagram, GHJK ≅ LMNP. Identify all pairs of congruent corresponding sides.
MN
HJ
NP
JK
LM
GH
LP
GK
In the diagram, GHJK ≅ LMNP. Write another congruence statement for the polygons. JHGK ≅ ____
NMLP
LMNP
PNML
PLMN
Find m∠V.
(a)
The figure shows the flag of the Czech Republic. What congruence statement can we write about its polygons? ABCF≅_____
ABCD
ABDE
FCDE
EDCF
Decide whether there is enough information to prove that △WXZ ≅ △YZX using the SAS Congruence Theorem. Explain your reasoning.
yes; Because ZW≅XY , ∠W≅∠Y , and WX≅YZ , the two triangles are congruent by the SAS Congruence Theorem.
yes; Because ZW≅XY , ∠W≅∠Y , and ZX≅XZ ,, the two triangles are congruent by the SAS Congruence Theorem.
no; There is one pair of congruent sides and one pair of congruent angles, but there is no other pair of congruent sides.
no; There are two pairs of congruent sides and one pair of congruent angles, but the angles are not the included angles.
Prove that △WXZ≅△YZX using the SAS congruence theorem.
In the pyramid-shaped picture frame shown, AD = CD and ∠ADB ≅ ∠CDB. Use the SAS Congruence Theorem to prove that △ADB ≅ △CDB. Fill in the missing statement for the proof.
Complete the statement. State which theorem you used. If QP≅QR , then ∠P≅ ____.
∠PRQ , Base Angles Theorem
∠Q , Vertical Angles Theorem
∠PRQ , Isosceles Triangle Theorem
∠QR , Corresponding Angles Theorem
Complete the statement. State which theorem you used. If ∠TRV ≅ ∠TVR, then TR≅ ______.
TV , Converse of Base Angles Theorem
TV , Base Angles Theorem
RV , ASA Congruence Theorem
RS , AAS Congruence Theorem
Find the values of x and y.
x = (a)
y = (b)
Find the values of x and y in the diagram.
x = (a)
y = (b)
Find the perimeter of the triangular hedge in feet.
Decide whether enough information is given to prove that △LMP ≅ △NPM using the SSS Congruence Theorem.
Decide whether enough information is given to prove that △WXZ ≅ △YZX using the HL Congruence Theorem.
What additional information do you need to prove that △ABD ≅ △CBD using the HL Congruence Theorem?
AD⊥AB
BD⊥AC
AB⊥AC
DB⊥BC
What additional information do you need to prove that △ABD ≅ △CBD using the SSS Congruence Theorem?
DC≅AB
AD≅DC
AB≅CB
AD≅CB
Decide whether enough information is given to prove that the triangles are congruent using the AAS Congruence Theorem, and why.
yes; It is given that ∠E ≅ ∠H, ∠F ≅ ∠J, and FG ≅ JK. So, △EFG ≅ △HJK by the AAS Congruence Theorem.
yes; It is given that ∠E ≅ ∠J, ∠F ≅ ∠H, and FG ≅ JK. So, △EFG ≅ △HJK by the AAS Congruence Theorem.
no; One of the pairs of congruent angles are not corresponding angles for the triangles. So, AAS does not apply in this case.
no; The information given applies to two angles and an included side. So, AAS does not apply in this case.
Decide whether enough information is given to prove that the triangles are congruent using the AAS Congruence Theorem, and why.
yes; It is given that ∠T ≅ ∠Q and UT ≅ RQ. Also, ∠V ≅ ∠S by the Symmetric Property of Congruence. So, △TUV ≅ △QRS by the AAS Congruence Theorem.
yes; It is given that ∠T ≅ ∠Q and UT ≅ RQ. Also, ∠V ≅ ∠S by the definition of acute angles of a triangle. So, △TUV ≅ △QRS by the AAS Congruence Theorem.
no; The given information applies to two angles and an included side. So, AAS does not apply in this case.
no; There is only enough information to conclude that one pair of angles and one pair of sides are congruent. So, AAS does not apply in this case.
Decide whether enough information is given to prove that the triangles are congruent using the ASA Congruence Theorem, and why.
yes; It is given that ∠PLN ≅ ∠MLN and ∠PNL ≅ ∠MNL. Also, LN ≅ LN by the Symmetric Property of Congruence. So, △LPN ≅ △LMN by the ASA Congruence Theorem.
yes; It is given that ∠PLN ≅ ∠MLN and ∠PNL ≅ ∠MNL. Also, LN ≅ LN by the Reflexive Property of Congruence. So, △LPN ≅ △LMN by the ASA Congruence Theorem.
no; The information given applies to two angles and a non-included side. So, ASA does not apply in this case.
no; There is only enough information to conclude that two pairs of angles are congruent. So, ASA does not apply in this case.
Decide whether enough information is given to prove that the triangles are congruent using the ASA Congruence Theorem, and why.
yes; It is given that WZ∥YX . ∠WXZ is supplementary to ∠ZWX and ∠WZX is supplementary to ∠YXZ by the Consecutive Interior Angles Theorem. Also, ZX ≅ ZX by the Reflexive Property of Congruence. So, △WXZ ≅ △YZX by the ASA Congruence Theorem.
yes; It is given that WZ∥YX ∠WXZ ≅ ∠YZX and ∠WZX ≅ ∠YXZ by the Alternate Interior Angles Theorem. Also, ZX ≅ ZX by the Reflexive Property of Congruence. So, △WXZ ≅ △YZX by the ASA Congruence Theorem.
no; There is only enough information to conclude that one pair of angles and one pair of sides are congruent. So, ASA does not apply in this case.
no; The information given applies to two angles and a non-included side. So, ASA does not apply in this case.
Explain how to prove that ∠K ≅ ∠N. △HJK≅ (a) by the (b) Congruence Theorem. Because
corresponding parts of congruent triangles are congruent, ∠K≅∠N .
△LMN
Explain how to prove that the statement is true.
AD≅CB
Write a plan to prove that ∠1 ≅ ∠2.
Order the steps to prove that ∠1 ≅ ∠2.
Use the ASA Congruence Theorem to prove that
△MFK≅△JHL .
Because corresponding parts of congruent triangles are
congruent, ∠2≅∠1 .
By the Symmetric Property of Congruence ∠1≅∠2 .
The diagram shows the shortest route around the buoys at points A, B, C, and D for a boat race. Use the information in the diagram to prove that ∠D ≅ ∠B.
Which is the most convenient placement of an isosceles triangle in the coordinate plane for finding the side lengths?
Which is the most convenient placement of a trapezoid with a pair of adjacent right angles in the coordinate plane for finding the side lengths?
A rectangle has vertices (0, 0), (2k, 0), and (0, k). Find the fourth vertex. The fourth vertex is
(2k,k)
(2k,2k)
(k,2k)
(k,k)
A square has vertices (−k, 0), (0, k), and (k, 0). Find the fourth vertex.
(0,−k)
(k,k)
(−k,k)
(k,−k)
Given Coordinates of vertices of △ODB and △BDC
Prove △ODB ≅ △BDC
Find DC . Explain your reasoning.
DC= (a) . The answer can be found using the (b)
Find RS . Explain your reasoning.
RS= (a) . The answer can be found using the (b)
Find m∠JFH . Explain your reasoning.
m∠JFH= (a) °. The answer can be found using the (b)
Is there enough information in the diagram to find ST ?
yes
no
Find the coordinates of the circumcenter of the triangle with the given vertices.
T( − 6,− 5), U(0,− 1), V(0,− 5)
(0,−1)
(−6,−3)
(−3,−5)
(−3,−3)
Find the coordinates of the circumcenter of the triangle with the given vertices.
X( − 2, 1), Y(2,− 3), Z(6,− 3)
(4,3)
(2,−2)
(3,1)
(0,−1)
Point D is the incenter of △LMN . Find the value of x .
Point D is the centroid of △ABC . Find ED and DC . EC=18
ED= (a)
DC= (b)
Find the coordinates of the centroid of the triangle with the given vertices.
A( − 10, 3), B( − 4, 5), C( − 4, 1)
(−8,3)
(−6,3)
(−7,2)
(−5,4)
Find the coordinates of the centroid of the triangle with the given vertices.
D(2,− 8), E(2,− 2), F(8,− 2)
(5,−3)
(4,−4)
(6,−6)
(3,−5)
Tell whether the orthocenter of the triangle with the given vertices is inside, on, or outside the triangle.
G(1, 6), H(5, 6), J(3, 1)
Find the coordinates of the orthocenter of the triangle with the vertices at:
G(1, 6), H(5, 6), J(3, 1)
(2,5)
(3,5.2)
(1,4)
(4,7)
Find the coordinates of the orthocenter of the triangle with the vertices at:
K( − 8, 5), L( − 6, 3), M(0, 5)
(−6,−1)
(−2,7)
(−2,11)
(−6,3)
Tell whether the orthocenter of the triangle with the given vertices is inside, on, or outside the triangle.
K( − 8, 5), L( − 6, 3), M(0, 5)
The centroid of △ABC lies on one of the altitudes of △ABC . What can you conclude about
△ABC ?
Triangle ABC is acute.
Triangle ABC is obtuse.
Plot the triangle with the vertices A(−6, 8), B(−6, 4), and C (0, 4) . Then plot its midsegment points.
Plot the triangle with the given vertices D(−3, 1), E( 3, 5), and F( 1,− 5). Then plot its midsegment points.
DE is a midsegment of △ABC . Find the value of x .
(a)
DE is a midsegment of △ABC . Find the value of x .
(a)
The diagram shows your first lap in mowing the triangular field. How far do you travel in this lap, in meters?
Order steps 2-6 of the indirect proof of the statement "In △XYZ , if XY=4 and XZ=8 , then YZ>4 ."
Then, it follows that either YZ < 4 or YZ = 4.
If YZ < 4 , then XY + YZ < XZ because 4 + YZ < 8 when YZ < 4.
If YZ = 4 , then XY + YZ = XZ because 4 + 4 = 8.
Both conclusions contradict the Triangle Inequality Theorem, which
says that XY + YZ > XZ.
So, the temporary assumption that YZ ≯ 4 cannot be true.
List the sides of the triangle in order from shortest to longest.
FH
FG
GH
List the sides of the triangle in order from shortest to longest.
JK
KL
JL
Describe the possible lengths of the third side (x) of the triangle if the lengths of the other two sides are 4
and 8.
(a)
Describe the possible lengths of the third side (x) of the triangle if the lengths of the other two sides are 6
and 9.
(a)
If RQ=RS and m∠QRT>m∠SRT , then how does QT compare to ST ?
QT (a) ST
>
If RQ=RS and QT>ST , then how does ∠QRT compare to ∠SRT ?
∠QRT (a) ∠SRT
>
Two boats leave the same island. The first boat travels 20 miles due south, then turns 20°
toward east and travels 15 miles. The second boat travels 15 miles due east, then turns 10°
toward north and travels 20 miles. Which boat is farther from the island?
Find the sum of the measures of the interior angles of a regular 30-gon. Then find the measure of each interior angle and each exterior angle.
The sum of the measures of the interior angles is (a) . The measure of each interior angle (b) and the measure of each exterior angle is (c) .
Find the value of x .
(a)
Find the value of x .
(a)
Find the value of x .
(a)
Find the value of each variable in the parallelogram.
a= (a)
b= (b)
28
87
Find the value of each variable in the parallelogram.
c= (a)
d= (b)
6
10
Find the coordinates of the intersection of the diagonals of parallelogram QRST with vertices Q( − 8, 1), R(2,1), S(4,− 3), and T( − 6,− 3) .
(−4,0)
(−2,−1)
(1,−2)
(0,2)
Three vertices of parallelogram JKLM are J(1, 4), K(5, 3), and L(6,− 3) . Find the coordinates of vertex M .
(3,1)
(2,−2)
(4,−1)
(0,2)
The figure shown is composed of two parallelograms. Find x .
(a)
State which theorem you can use to show that the quadrilateral is a parallelogram.
Definition of a Parallelogram
Parallelogram Opposite Sides Theorem
Parallelogram Opposite Angles Converse
Parallelogram Opposite Sides Converse
State which theorem you can use to show that the quadrilateral is a parallelogram.
Parallelogram Opposite Sides Theorem
Definition of a Parallelogram
Parallelogram Diagonals Theorem
Parallelogram Diagonals Converse
State which theorem you can use to show that the quadrilateral is a parallelogram.
Parallelogram Opposite Angles Converse
Parallelogram Opposite Angles Theorem
Definition of a Parallelogram
Parallelogram Consecutive Angles Theorem
Find the values of x and y that make the quadrilateral a parallelogram.
x= (a)
y= (b)
1
6
Find the value of x that makes the quadrilateral a parallelogram.
x= (a)
4
In the diagram of the staircase shown, QT∥RS , QT=RS=9 feet, QR=3 feet, and m∠QRS=123° .
Which theorem can you use to show that QRST is a parallelogram?
Parallelogram Opposite Angles Theorem
Opposite Sides Parallel and Congruent Theorem
Parallelogram Opposite Angles Converse
Parallelogram Diagonals Theorem
Show that quadrilateral WXYZ with vertices W( − 1,6), X(2, 8), Y(1, 0), and Z( − 2, − 2) is a parallelogram by finding the indicated slopes and side lengths.
slope of WX= (a) = slope of YZ
WX= (b) =YZ
Quadrilateral WXYZ is a parallelogram by the (c)
32
13
Classify the special quadrilateral as specifically as possible. Explain your reasoning.
parallelogram; There are two pairs of parallel sides.
rhombus; There are four congruent sides.
square; There are four congruent sides.
rectangle; There are two pairs of opposite congruent sides.
Classify the special quadrilateral as specifically as possible. Explain your reasoning.
parallelogram; There are two pairs of parallel sides.
parallelogram; There are two pairs of opposite congruent sides.
rectangle; There are two pairs of parallel sides.
rectangle; There are two pairs of opposite congruent sides.
Classify the special quadrilateral as specifically as possible. Explain your reasoning.
parallelogram; There are two pairs of parallel sides.
rhombus; There are four congruent sides and opposite angles are congruent.
square; There are four congruent sides and the angles are 90°.
rectangle; There are two pairs of opposite congruent sides and the angles are 90°.
Find the lengths of the diagonals of rectangle WXYZ where WY=−2x+34 and XZ=3x−26 .
Decide whether parallelogram JKLM with vertices J(5, 8), K(9, 6), L(7, 2), and M(3, 4) is a
rectangle, a rhombus, or a square. Select all names that apply.
rectangle
rhombus
square
kite
Find the measure of ∠W in the isosceles trapezoid WXYZ .
144°
122°
32°
58°
Find the length of the midsegment of trapezoid ABCD.
Find the exact length of the midsegment of trapezoid JKLM with vertices J(6, 10), K(10, 6), L(8, 2), and M(2, 2) .
A kite has angle measures of 7x°, 65°, 85°, and 105°. Find the value of x .
(a)
Quadrilateral WXYZ is a trapezoid with a pair of opposite supplementary angles. Is WXYZ
an isosceles trapezoid?
Give the most specific name for the quadrilateral. Explain your reasoning.
parallelogram; Opposite sides are parallel.
trapezoid; There is one pair of parallel sides.
quadrilateral; There is not enough information to classify it more specifically.
isosceles trapezoid; There is one pair of parallel sides so the legs are congruent.
Give the most specific name for the quadrilateral. Explain your reasoning.
kite; Consecutive sides are congruent.
square; There are four congruent sides.
rectangle; Opposite sides are congruent.
rhombus; There are four congruent sides.
Give the most specific name for the quadrilateral.
Quadtilateral
In kite ABCD , m∠DAE=52° , what is m∠ABE ?
180°
90°
38°
42°
In kite ABCD, if BE=5y−5 and ED=y+19 , what is DB?
6
24
25
50
