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Tenth Grade (Grade 10) Geometry and Measurement Questions

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

What is the missing reason in step 4 of the following proof?

Given: Quadrilateral [math]ABCD[/math] where [math]bar{AD}[/math] || [math]bar{BC}[/math] and [math]bar{AD} ~= bar{BC}[/math]
Prove: [math]bar{AB} " || " bar{CD}[/math]

Parallelogram ABCD v3

[math] \ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \ [/math]	[math] " Reason "[/math]
[math]1. bar{AD} " \|\| " bar{BC} [/math]	[math]1. "Given"[/math]
[math]2. ang CBD ~= ang ADB [/math]	[math]2. "Alternate interior angles are congruent"[/math]
[math]3. bar{BC} ~= bar{AD}[/math]	[math]3. "Given"[/math]
[math]4. bar{BD} ~= bar{BD} [/math]	[math]4. ""[/math]
[math]5. Delta ABD ~= Delta CDB [/math]	[math]5. "Side-Angle-Side Postulate"[/math]
[math]6. ang ABD ~= ang CDB [/math]	[math]6. "Corresponding angles of congruent triangles are congruent"[/math]
[math]7. bar{AB} " \|\| " bar{CD}[/math]	[math]7. "If two lines are cut by a transversal, and alternate interior"[/math] [math] \ \ \ \ \ " angles are congruent, the lines are parallel"[/math]

Reflexive Property
Diagonals of a parallelogram are congruent
Given by the diagram
Corresponding sides of congruent triangles are congruent

Grade 10 Pythagorean Theorem and Applications

Using the following measurements, find the length of the leg of the right triangle.
leg = 5
hypotenuse = 13

12
13
144

Grade 10 Pythagorean Theorem and Applications

Using the measurements given below, find the hypotenuse of the triangle.
Leg = 20 units
Leg = 21 units

400 units
841 units
29 units

Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.4

For the circle centered at [math](-1,3)[/math] with radius 3, which of the following is true about the point [math](0.5, 0.2) ?[/math]

It lies on the circle.
It lies in the circle.
It lies outside the circle.
Not enough information.

Grade 10 Circles

For each part of the circle listed below, choose ALL of the properties which are true about it.

	Always intersects the center of the circle	Touches only ONE point on the circle	Can form inscribed angles
Radius
Diameter
Tangent
Chord

Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9

Choose the correct missing reason from step 3.

Given the parallel lines [math]k[/math] and [math]m[/math], and transversal [math]t[/math], prove that [math]ang 1 ~= ang 7[/math].

Parallel Lines - Skew Transversal

[math] \ \ \ \ \ \ " Statement " \ \ \ \ \ \ [/math]	[math] " Reason "[/math]
[math]1. k " \|\| " m[/math]	[math]1. "Given"[/math]
[math]2. ang 1 ~= ang 5[/math]	[math]2. "Corresponding angles are congruent"[/math]
[math]3. ang5 ~= ang 7 [/math]	[math]3. [/math]
[math]4. ang 1 ~= ang 7 [/math]	[math]4. "Substitution property of equality"[/math]

Vertical angles are congruent
Given
Same side interior angles are congruent
Supplementary angles are congruent

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2

How is the transformation between the two graphs best described?
Graph - Linear Function y=1/2x

translation
rotation
reflection
reflection and rotation

Grade 10 Triangles

What is the definition of complimentary angles?

Two angles that add to be [math]180 deg[/math]
Two angles that have a difference of [math]90 deg[/math]
Two angles add to be [math]90 deg[/math]
Two angles that have a difference of [math]180 deg[/math]

Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9

Choose the correct missing reason from step 4.

Given that [math]k[/math] and [math]m[/math] are parallel, and that line [math]t[/math] is a transversal, prove that [math]ang 1[/math] and [math] ang 6[/math] are supplementary.

Parallel Lines - Skew Transversal

[math] " Statement " [/math]	[math] " Reason "[/math]
[math]1. k " \|\| " m[/math]	[math]1. "Given"[/math]
[math]2. ang 1 ~= ang 5[/math]	[math]2. "Corresponding angles are congruent"[/math]
[math]3. m ang 1 = m ang 5 [/math]	[math]3. "Definition of congruent angles"[/math]
[math]4. m ang 5 + m ang 6 = 180°[/math]	[math]4. [/math]
[math]5. m ang 1 + m ang 6 = 180°[/math]	[math]5. "Substitution property of equality"[/math]
[math]6. ang 1 " and " ang 6 " are supplementary" [/math]	[math]6. "Definition of supplementary angles"[/math]

Same side interior angles are supplementary
From the diagram
Linear pairs of angles are supplementary
Given

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

What is the missing reason in step 6?

Given: [math]ang BAC ~= ang BCA[/math] and [math]bar{BD} _|_ bar{AC}[/math] (point [math]D[/math], the intersection of the altitude from B to [math]bar{AC}[/math] not shown)
Prove: [math]bar{AB} ~= bar{BC}[/math]

Equilateral Triangle Height v1

[math] \ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \ [/math]	[math] " Reason "[/math]
[math]1. ang BAC ~= ang BCA [/math]	[math]1. "Given"[/math]
[math]2. bar{BD} _\|_ bar{AC} [/math]	[math]2. "Given"[/math]
[math]3. ang BDA, ang BDC " are right angles"[/math]	[math]3. "Definition of perpendicular lines"[/math]
[math]4. ang BDA = ang BDC [/math]	[math]4. "All right angles are congruent"[/math]
[math]5. bar{BD} ~= bar{BD} [/math]	[math]5. "Reflexive Property"[/math]
[math]6. Delta BDA ~= Delta BDC [/math]	[math]6. ""[/math]
[math]7. bar{BA} ~= bar{BC}[/math]	[math]7. "Corresponding sides of congruent triangles are congruent"[/math]

Side-Side-Side Postulate
Hypotenuse-Leg Postulate
Angle-Angle-Side Postulate
Angle-Side-Angle Postulate

Grade 10 Angles

Which of these is not a type of angle?

acute
obtuse
skew
right

Grade 10 Three Dimensional Shapes

Match each three dimensional shape with a fact that is true about it.

__	Triangular Pyramid	A.	Its volume is the length of any side raised to the power of 3.
__	Sphere	B.	All points on its surface are equidistant from its center.
__	Cube	C.	It has four vertices.
__	Cylinder	D.	It has two edges but no vertices.

Grade 10 Angles

An angle that measures exactly 90 degrees.

acute
obtuse
straight
complementary
none of the above

Grade 10 Circles CCSS: HSG-C.A.4

Which line segment is tangent to circle O?

[math]bar(AB[/math]
[math]bar(AC[/math]
[math]bar(AD[/math]
[math]bar(AO[/math]

Grade 10 Angles

An angle that measures between 0 and 90 degrees.

acute
complementary
right
straight
none of the above

Grade 10 Three Dimensional Shapes

For the shape below, define:

A. Volume: 672 cm cubed

B. Surface Area: 528 cm squared

Grade 10 Similar and Congruent Figures

A triangle where [math]ang B = 30°[/math] will be similar to a triangle where [math]ang C = 60°.[/math]

Always
If the side lengths are the same
If they are right triangles
Never

Grade 10 Points, Lines, and Planes

Points contained on the same line.

coplanar
collinear
line
plane

Grade 10 Similar and Congruent Figures

In the following diagram, quadrilaterals ABED and BFDC are both parallelograms. Match the sides or angles which are congruent.

__	[math]bar{AB}[/math]	A.	[math]ang 2[/math]
__	[math]ang A[/math]	B.	[math]bar{ED}[/math]
__	[math]ang 1[/math]	C.	[math]ang E[/math]
__	[math]bar{AC}[/math]	D.	[math]ang DFE[/math]
__	[math]ang BCA[/math]	E.	[math]bar{FE}[/math]

Grade 10 Quadrilaterals

For each of the five quadrilaterals listed below, choose all of the correct properties of their diagonals.

	Diagonals Bisect Each Other	Diagonals are Perpendicular	Diagonals are Congruent
Square
Rectangle
Parallelogam
Rhombus
Kite
Isosceles Trapezoid

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Tenth Grade (Grade 10) Geometry and Measurement Questions