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Tenth Grade (Grade 10) Two Dimensional Shapes Questions

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Grade 10 Triangles

In the triangle, angle A = 95 degrees, and angle B = 25 degrees. It is possible for side AB to be the longest side of the triangle.

True
False

Grade 10 Triangles CCSS: HSG-CO.B.8

SSS can prove that two triangles are congruent.

True
False

Grade 10 Other Polygons CCSS: HSG-SRT.C.8, HSG-MG.A.1

Shawn wants to install a new fence around his property. The fencing costs $50 per meter. The shape of his property is shown below. The lengths of some of the property edges are

$AB = 30 \ "m"$ ,

$BC = 45 \ "m"$ ,

$EF = 13 \ "m"$ , and

$DE = 20 \ "m"$ . How much will it cost to fence his yard, rounded to the nearest dollar?

$8,310
$8,960
$9,560
$9,809

Grade 10 Circles

If point A is equidistant from all of the points in the circle, what is point A called?

the midpoint
the focus
the center
the point
the middle

Grade 10 Circles

A line in the plane of a circle that intersects the circle in exactly one point.

perimeter
circumference
bisector
tangent

Grade 10 Triangles CCSS: HSG-CO.B.8

SAS can prove that two triangles are congruent.

True
False

Grade 10 Circles

For the proof shown, choose the correct reasons for steps 4 and 6.

Given: The circle pictured with diameter

$bar{AD}$ (not drawn), with

$bar{AB}$ tangent to the circle, and line

$bar{AC}$ also not drawn.
Prove:

$triangle ABD \ ~ triangle CAD$ .

Circle with Secant CD and Tangent AB

$" Statement "$	$" Reason "$
$1. "Draw " bar(AD) \ & \ bar{AC}$	$1. "Two points create a line"$
$2. bar(AD) \ \ "is a diameter"$	$2. "Given"$
$3. ang ACD \ \ "is a right angle"$	$3. "Inscribed angle subtended by a diameter is a right angle"$
$4. bar(AB) \ \ "is tangent to the circle"$	$4.$
$5. bar{AB} _\|_ bar{AD}$	$5. "A tangent line is perpendicular to the diameter"$
$6. ang BAD \ \ "is a right angle"$	$6.$
$7. ang ACD ~= ang BAD$	$7. "All right angles are congruent"$
$8. ang ADC ~= ang ADB$	$8. "Reflexive property"$
$9. triangle ABD \ ~ triangle CAD$	$9. "AA"$

Looks correct; Definition of perpendicular lines
Given; Triangle ABD is a right triangle
Definition of a Tangent; Looks correct
Given; Definition of perpendicular lines

Grade 10 Quadrilaterals

For each of the quadrilaterals listed below, choose all correct properties about their sides.

	At Least One Pair of Opposite Sides is Congruent	At Least Certain Adjacent Pairs of Sides are Congruent	At Least One Pair of Opposite Sides is Parallel
Square
Rectangle
Parallelogram
Rhombus
Kite
Isosceles Trapezoid

Grade 10 Other Polygons

The radius of a regular polygon is also the radius of the circle circumscribed about that polygon.

True
False

Grade 10 Circles

Which is an inscribed angle?

$ang CAB$
$ang ADO$
$ang DAB$
$ang BOD$

Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

What is the missing reason in step 8 of the following proof?

Given: Quadrilateral

$ABCD$ with diagonal

$bar{BD}$ where

$bar{AB}$ ||

$bar{CD}$ and

$bar{BC}$ ||

$bar{AD}$
Prove:

$ang BAD ~= ang DCB$

Parallelogram ABCD v3

$\ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \$	$" Reason "$
$1. bar{AB}$ \|\| $bar{CD}$	$1. "Given"$
$2. ang ABD ~= ang CDB$	$2. "Alternate interior angles are congruent"$
$3. bar{BC}$ \|\| $bar{AD}$	$3. "Given"$
$4. ang ADB ~= ang CBD$	$4. "Alternate interior angles are congruent"$
$5. m ang ABD = m ang CDB, \ \ m ang ADB = m ang CBD$	$5. "Definition congruent angles"$
$6. m ang ABD + m ang ADB + m ang BAD = 180°,$ $\ \ \ \ \ \ \ \ \ m ang CDB + m ang DCB + m ang CBD = 180°$	$6. "Sum of angles in a triangle is 180°"$
$7. m ang CDB + m ang DCB + m ang CBD =$ $\ \ \ \ \ \ \ \ \ \ m ang ABD + m ang ADB + m ang BAD$	$7. "Substitution Property of Equality"$
$8. m ang DCB = m ang BAD$	$8. ""$
$9. ang BAD ~=ang DCB$	$9. "Definition of congruent angles"$

Elimination Property of Equality
Corresponding angles are congruent
Definition of congruent terms
Subtraction Property of Equality

Grade 10 Other Polygons CCSS: HSG-MG.A.2

Sean is making cards for an upcoming event. The cards will be in the shape of a regular octagon, where there are two octagons attached by one edge. One edge of the octagonal card measures

$5 \ "cm"$ . If the paper density is

$100 \ "g"//"m"^2$ , and Sean makes 100 cards, what is the total mass of all the cards, rounded to the nearest gram?

241 g
385 g
483 g
24,140 g

Grade 10 Circles

What are the missing reasons in steps 2 and 6 for the proof?

Given the circle shown, where

$m \stackrel{\frown}{EB} = m \stackrel{\frown}{DC}$ and with

$bar{EC}, bar{BD}, & \ bar{ED}$ not drawn, prove that

$triangle EBD ~= triangle DCE$ .

Circle with Two Secants ABCDE

$" Statement "$	$" Reason "$
$1. "Draw " bar{EC}, bar{DB}, & \ bar{ED}$	$1. "Two points define a line"$
$2. m \stackrel{\frown}{EB} = m \stackrel{\frown}{DC}$	$2.$
$3. m ang EDB = 1/2 m \stackrel{\frown}{EB}$	$3. "Measure of inscribed angle is 1/2 the measure of intercepted arc"$
$4. m ang CED = 1/2 m \stackrel{\frown}{CD}$	$4. "Measure of inscribed angle is 1/2 the measure of intercepted arc"$
$5. 1/2 m \stackrel{\frown}{EB} = 1/2 m \stackrel{\frown}{DC}$	$5. "Multiplicative Property of Equality"$
$6. m ang EDB = m ang CED$	$6.$
$7. ang EDB ~= ang CED$	$7. "Definition of congruent angles"$
$8. ang EBD ~= ang ECD$	$8. "Inscribed angles intercepting the same arc are congruent"$
$9. bar{ED} ~= bar{ED}$	$9. "Reflexive Property"$
$10. triangle EBD ~= triangle DCE$	$10. "AAS"$

Given; Substitution Property of Equality
Assume from diagram; Closure Property of Addition
Given; Addition Property of Equality
Assume from diagram; Closure Property of Multiplication

Grade 10 Circles

What is the radius of a circle with a circumference of 56.52 m?

7 m
9 m
18 m
14 m

Grade 10 Triangles

This triangle is a(n) triangle.
Side 1: 6
Side 2: 11
Side 3: 14

Right
Acute
Obtuse

Grade 10 Other Polygons

An apothem connects two sides of a regular polygon.

True
False

Grade 10 Other Polygons CCSS: HSG-MG.A.1

Casey is mowing her neighbor's lawn. The below figure gives the approximate shape of the lawn, where

$AB = 110 \ "yd", \ BC = 71 \ "yd", \ CD = 67 \ "yd"$ and

$AF = 45 \ "yd"$ . There are 100 trees planted randomly on the lawn, all at least a few yards away from each other or the edges of the lawn. At the base of each tree is a circular region, approximately

$2.5 \ "yd"$ in diameter, where there is no grass. If it takes Casey about 10 minutes to mow every 400 square yards, how long does it take her to mow her neighbor's lawn? Round the answer to the nearest minute.

1 hour and 58 minutes
2 hours and 35 minutes
2 hours and 47 minutes
3 hours and 3 minutes

Grade 10 Quadrilaterals CCSS: HSG-CO.C.11

What is the missing statement in step 4 in the following proof?

Given that

$ABCD$ is a rectangle, prove that

$bar{AC}~=bar{BD} \ \$ (

$bar{AC}, bar{BD}$ not pictured).

Rectangle ABCD

$\ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \$	$" Reason "$
$1. ABCD " is a rectangle"$	$1. "Given"$
$2. bar{AB} ~= bar{CD}$	$2. "Opposite sides of a rectangle are congruent"$
$3. ang ABC, ang BCD " are right angles"$	$3. "Interior angles of rectangles are all right angles"$
$4.$	$4. "All right angles are congruent"$
$5. bar{BC} ~= bar{BC}$	$5. "Reflexive Property"$
$6. Delta ABC ~= Delta DCB$	$6. "Side-Angle-Side Postulate"$
$7. bar{AC} ~= bar{BD}$	$7. "Corresponding sides of congruent triangles are congruent"$

$ang ABC ~= ang CDA$
$ang BAD ~= ang BCD$
$ang BAD ~= ang CDA$
$ang ABC ~= ang BCD$

Grade 10 Triangles

Which of the following two triangles may not be congruent?

Both having three same lengths
Two angles and a corresponding side are equal
Two angles and the included side of both triangles are equal
If two sides and the angle attached to one length are equal

Grade 10 Triangles CCSS: HSG-CO.C.10

This question is a part of a group with common instructions. View group »

What is the missing statement in step 7?

$triangle ABD ~= triangle BDC$
$triangle ABD ~= triangle DBC$
$triangle ABD ~= triangle CDB$
$triangle ABD ~= triangle CBD$

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Tenth Grade (Grade 10) Two Dimensional Shapes Questions