2. A) Name and Measure the Angles Marked with Arcs

1. Identify the object as a line, ray, or line segment. Name the object.

a)b) c)

______

2. a) Name and measure the angles marked with arcs.

i) ______= ______

ii) ______= ______

Bonus► Name the quadrilateral in three ways.

______

3.Mark the parallel sides and the right angles. Then identify the type of quadrilateral.

a)b)c)

______

4.a) Use a protractor and the given line segment to draw ABC = 42.

b) Draw a line perpendicular to AB through point A.

1. / a) / line segment AD or
line segment DA
b) / line BE or line EB
c) / ray FC
2. / a) / i) / GMN = 112º
ii) / NHM = 62º
Bonus
Answers will vary.
Sample answer:
MNHG, MGHN, NMGH
3. / a) /




rectangle
b) / trapezoid
c) /


parallelogram
4. / Teacher to check.

1.Find the measure of the missing angle.

a)b)

______

______

______

2.One angle of an isosceles triangle is 36. Find the measures of the other angles.

Hint: Make sketches to show the different options for placing the 36 angle.

3. Write “true” or “false.” If the statement is false, give a counterexample.

a) The opposite angles in any
parallelogram are equal. / b) All scalene triangles are right triangles.

Bonus► Triangle MNO has M = 90, and N = 45. Classify the triangle.

1. / a) / B = 180º − (90º
+ 58º)
= 180º − 148º
= 32º
b) / H = 180º − (23º
+ 35º)
= 180º − 58º
= 122º
2. / A triangle with angles 36º, 36º, and 108º.
A triangle with angles 36º, 72º, and 72º
3. / a) / true
b) / false
Counterexamples may vary. Teacher to check.
Bonus
O = 180º − 90º − 45º
= 45º
MNO is a right isosceles triangle.

1.Match the diagram to the correct description.

A. B. C.

a) The rays intersect. ______

b) If the rays are extended far enough, they intersect. ______

c) The rays do not intersect, even if they are extended. ______

2. a) Draw lines perpendicular to CD through points M and N. Label the intersection points.

b) Draw line segment MN. Name the quadrilateral you created. ______

c) Classify the quadrilateral. ______

3. Measure the sides and the angles in the polygon. Mark the equal sides and
equal angles. Then classify the polygon. Be as specific as you can.

a)b)

______

4. Find the measure of the missing angle.

a)b)

5. One side of an isosceles triangle is 5 cm. The perimeter of the triangle is 13 cm.
What are thelengths of the sides of the triangle?Make sketches to show the
different options for placing the side that is 5 cm long.

6. If the statement is true, explain why. If the statement is false, give a counterexample.

a) If a triangle is equilateral, its angles are all equal to 60.

b) A trapezoid cannot have two equal opposite sides.

Bonus► Can a triangle have two right angles? Explain.

1. / a) / A
b) / C
c) / B
2. / a) / Teacher to check.
b) / Sample answer:
CMND
c) / trapezoid or
right trapezoid
3. / a) / 29 mm
29 mm
29 mm
29 mm
rhombus
b) / 26 mm
4 cm
5 cm
scalene obtuse triangle
4. / a) / A = 180º − (28º
+ 90º)
= 180º − 118º
= 67º
b) / R + Q = 180º − 28º
= 152º
R = Q = 152º ÷ 2
= 76º
5. /
5 cm 5 cm
3 cm

4 cm 4 cm
5 cm
6. / a) / true
Sample answer:
The angles in an equilateral triangle are all equal. The sum of the angles in a triangle is 180º, so each angle equals 180º ÷ 3 = 60º.
b) / false
Sample counterexample:


Bonus
No. The angles in a triangle add to 180º. If two of the angles are right angles, then 90º + 90º = 180º, so the third angle measures zero. This doesn’t make a triangle.

1.The triangles shown are congruent. Identify the equal sides
and equal angles. Then write the congruence statement.

______= ______, ______= ______,

______= ______,______= ______,

______= ______, ______= ______

Congruence statement: ______

2. a) What is the measure of DBC? _____
How do you know?

b) Write the pairs of equal sides and equal angles
in triangles AEB and BCD.

______= ______

______= ______

______= ______

Triangles AEB and BCD are congruent by the ______congruence rule.

c) DC = _____ = _____ cm

d) Which angle in AEB equals BDC? ______

What is the measure of these angles? ______

Bonus► What is the measure of the third pair of angles in triangles AEB and BCD? Explain.

1. / AB = FE
BD = EC
AD = FC
A = F
B = E
D = C
△ABD≅△FEC
2. / a) / 70º
DBC and ABE are vertical angles, so they are equal.
b) / BE = CE
AB = DB
ABE = DBC
SAS
c) / AE, 4.9
d) / EAB
75º
Bonus
Angles in a triangle add to 180º, so
E = 180º − (A
+ EAB)
= 180º − (75º
+ 70º)
= 35º
△AEB≅△DCB,
so E = C,
so C = 35º

1.Find the missing angle. Show your work

a)b)

x = ______x = ______

2. Find the missing alternate, corresponding, supplementary, or vertical angles.

a) b)

x = ______, y = ______x = ______, y = ______

3.Lines ℓ and m are parallel. Use what you know about corresponding and supplementary angles to explain
why x + y = 180°.

Bonus► Zara says thatAE is parallel to CD.
Is she correct? Explain.

1. / a) / x = 90º + 29º
= 119º
b) / x = 76º ÷ 2
= 38º
2. / a) / x = 61º
y = 119º
b) / x = 46º
y = 134º
3. / z and x are corresponding angles, so z = x.
y and z are supplementary angles, so y + z = 180º.
y + x = y + z = 180º
Bonus
Yes. ABE = DBC since they are vertical angles.
AB = BD and EB = CB
By the SAS rule,
△ABE ≅△DBC, so
EAB = CDB. These are alternate angles at lines AE and CD. When alternate angles are equal, lines are parallel, so AE∥CD.

1.Use the congruence statement ABCXYZPQR and A = 50, Y = 60
tofind the measures of all angles in all three triangles.

2. Identify the congruence rule that tells you that the pair of triangles is congruent.

a)b) c)

Congruence rule: ______Congruence rule: ______Congruence rule: ______

3. Fill in allthe missing angles. Mark parallel lines if they are not marked already.

a) b) c)

4. Use congruent triangles to explain why MON is isosceles.

5.Are the quadrilaterals congruent? Use a ruler and a protractor to check.
If yes, write the pairs of corresponding equal sides and corresponding
equal angles. Then write the congruence statement.

Bonus► Use the grid to draw a counterexample to this statement:

If triangles ABC and DEF have AB = DE, BC = EF,
and A = D, they are congruent.

Hint: Sketch the triangles first.

1. / A = X = P = 50º
B = Y = Q = 60º
C = Z = R = 180º −
(50º + 60º)
= 180º − 110º
= 70º
2. / a) / ASA
b) / SAS
c) / SSS
3. / a) /
b) /
c) /
4. / ML = NL
LO = OL
MLO = NLO = 90º
By the SAS rule,
△MOL≅△NOL,
soMO = NO and
△MONis isosceles.
5. / AB = WU
BC = UX
CD = XV
AD = WV
A = W
B = U
C = X
D = V
ABCD≅WUXV
Bonus
/ Answers may vary. Teacher to check.
Sample answer: