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Tenth Grade (Grade 10) Quadrilaterals 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

$ABCD$ where

$bar{AD}$ ||

$bar{BC}$ and

$bar{AD} ~= bar{BC}$
Prove:

$bar{AB} " || " bar{CD}$

Parallelogram ABCD v3

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

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

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
Parallelogram
Rhombus
Kite
Isosceles Trapezoid

Grade 10 Quadrilaterals

Which properties of parallelogram ABCD are true?

Sides AB and DC are parallel.
Angles B and C are supplementary.
Angle A equals Angle C.
The sum of all the angles is 360 degrees.
All of the above

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

What is the missing statement in step 6 of the following proof?

Given: Quadrilateral

$ABCD$ with diagonal

$bar{BD}$ where

$bar{AB}$ ||

$bar{CD}$ and

$bar{BC}$ ||

$bar{AD}$
Prove:

$bar{AB} ~= bar{CD}$

Parallelogram ABCD v4

$\ \ \ \ \ \ \ \ \ \ \ \ " Statement " \ \ \ \ \ \ \ \ \ \ \ \$	$" Reason "$
$1. bar{AB}$ \|\| $bar{CD}$	$1. "Given"$
$2. ang ABD ~= ang CDB$	$2. "Alternate interior angles are congruent"$
$3. bar{BC}$ \|\| $bar{AD}$	$3. "Given"$
$4. ang ADB ~= ang CBD$	$4. "Alternate interior angles are congruent"$
$5. bar{BD} ~= bar{BD}$	$5. "Reflexive Property"$
$6.$	$6. "Angle-Side-Angle Postulate"$
$7. bar{AB} ~= bar{CD}$	$7. "Corresponding sides of congruent triangles are congruent"$

$Delta ABC ~= Delta ACD$
$Delta ABD ~= Delta CDB$
$Delta ABC ~= Delta CDA$
$Delta ABD ~= Delta DCB$

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 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 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 Quadrilaterals

Which of the following pairs of quadrilaterals always have all 4 sides congruent?

square and rectangle
square and rhombus
rhombus and rectangle
parallelogram and square

Grade 10 Quadrilaterals

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

	At Least Certain Adjacent Angle Pairs are Supplementary	At Least One Pair of Opposite Angles is Congruent	At Least Certain Adjacent Angle Pairs are Congruent
Square
Rectangle
Parallelogram
Rhombus
Kite
Isosceles Trapezoid

Grade 10 Quadrilaterals

Which of the following pairs of quadrilaterals always have congruent diagonals?

square and parallelogram
square and rhombus
square and rectangle
parallelogram and rhombus

Grade 10 Quadrilaterals

Which of the following pairs of quadrilaterals always have perpendicular diagonals?

square and rectangle
parallelogram and rhombus
rhombus and rectangle
rhombus and square

Grade 10 Quadrilaterals

Which of the following is a valid conclusion?

All rhombi are squares.
All rhombi are rectangles.
All quadrilaterals are parallelograms.
All rectangles are parallelograms.

Grade 10 Quadrilaterals CCSS: HSG-SRT.C.8, HSG-MG.A.2

Most modern TV monitors are composed of many pixels, or picture elements. Full HD monitors typically have a resolution of 1920 x 1080 pixels. However, the clarity of images on the monitor depends on the pixel density- the number of pixels per square inch. If two screens are both full HD, but one is slightly larger than the other, the smaller screen will have a slightly clearer image because the pixel density will be greater. What is the pixel density on a full HD TV screen that is 32 inches large, and has a aspect ratio (or ratio of width to height) of 16:9? Round the answer to the nearest pixel per square inch. Note: the size of a TV screen is typically the distance between non-adjacent corners.

1,361 pixels per square inch
4,739 pixels per square inch
8,456 pixels per square inch
25,600 pixels per square inch

Grade 10 Quadrilaterals

Which of the following is NOT true for all parallelograms?

opposite sides are congruent
opposite angles are congruent
diagonals bisect each other
consecutive angles are congruent

Grade 10 Quadrilaterals

A rhombus is a type of isosceles trapezoid.

True
False

Grade 10 Quadrilaterals CCSS: HSG-SRT.B.5

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

What is the missing reason in step 12?

If 2 parallel lines are cut by a transversal, alternate angles are supplementary
If 2 parallel lines are cut by a transversal, consecutive exterior angles are supplementary
If 2 parallel lines are cut by a transversal, alternate interior angles are congruent
If 2 parallel lines are cut by a transversal, consecutive interior angles are supplementary

Grade 10 Quadrilaterals CCSS: HSG-SRT.B.5

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

What is the missing statement in step 8?

$ang AFB ~= ang BFE$
$ang AFB ~= ang EDC$
$ang BAF ~= ang EDC$
$ang BAF ~= ang ECD$

Grade 10 Quadrilaterals CCSS: HSG-SRT.B.5

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

What is the missing reason in step 16?

The sum of four non-obtuse angles is 360°
The sum of the interior angles of any two dimensional figure is 360°
Four angles make a full rotation, which is 360°
The sum of the interior angles in a quadrilateral is 360°

Grade 10 Quadrilaterals

In quadrilateral ABCD, if

$AB~=CD$ and

$AD~=BC$ , then diagonals AC and BD must .

be parallel
be perpendicular
bisect each other
be congruent

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

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

What is the missing reason in step 10?

Double Angle Identity
Supplementary angles
From the diagram
Substitution Property of Equality

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Tenth Grade (Grade 10) Quadrilaterals Questions