Quadrilaterals and Parallelograms
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Questions and Answers

What do you call a closed plane figure consisting of four side?

  • Quadrilateral (correct)
  • Triangle
  • Hexagon
  • Pentagon

Which of the following quadrilaterals is NOT a parallelogram?

  • Square
  • Trapezoid (correct)
  • Rectangle
  • Rhombus

HOME is a parallelogram. Which of the figures below illustrates the statement correctly?

  • Image C
  • Image D
  • Image B
  • Image A (correct)

How do you describe any two opposite angles in a parallelogram?

<p>They are supplementary. (B)</p> Signup and view all the answers

Which of these statements is NOT true about parallelograms?

<p>Opposite angles of a parallelogram are always supplementary. (C)</p> Signup and view all the answers

Using the figure on the right, what is m ∠ SRQ?

<p>45° (A)</p> Signup and view all the answers

WXUV is a parallelogram, what is m ∠ WVU?

<p>80° (D)</p> Signup and view all the answers

ABCD is a rhombus. Diagonals AC and BD intersect each other at E. If AE = 12, what is AC?

<p>24 (D)</p> Signup and view all the answers

What is m∠ AED?

<p>90° (D)</p> Signup and view all the answers

In parallelogram GRAM, <G = 5x + 15, <R = 17x – 11, what is the measure of <G?

<p>65° (B)</p> Signup and view all the answers

Use the figure on the right. If AB is twice of AD and AD is 10 cm, how long is AB?

<p>20 cm (C)</p> Signup and view all the answers

Square MATH has a side that measures 27 cm. Which of the following is NOT true?

<p>MA=AT = MT (C)</p> Signup and view all the answers

ABCD is a rhombus. If AB = (2x – 1) cm while CD = (x + 8) cm, what is the length of AB?

<p>17 cm (A)</p> Signup and view all the answers

MATH is a rectangle with diagonals MT and AH meet at S. Which segment that TH is congruent?

<p>MA (A)</p> Signup and view all the answers

Given: LOVE is rectangle with diagonals LV and OE meet at S. Which statement is true?

<p>LO = VE (B)</p> Signup and view all the answers

If m∠GIF = 112, then what is m∠IFT?

<p>68° (B)</p> Signup and view all the answers

Which of the statements is NOT true about a square?

<p>Opposite sides are perpendicular. (D)</p> Signup and view all the answers

Using the figure on the right, find the value of x.

<p>5 (B)</p> Signup and view all the answers

Flashcards

Quadrilateral Definition

A closed, two-dimensional shape with four sides.

Parallelogram Definition

A quadrilateral with two pairs of parallel sides.

Consecutive Angles

Angles that share a common side and vertex in a polygon.

Opposite Angles

Angles sitting opposite each other, formed by two intersecting lines.

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Supplementary Angles

Angles that add up to 180 degrees.

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Rhombus

A parallelogram with four congruent sides.

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Perpendicular Lines

Lines that meet at a 90-degree angle.

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Rectangle

A parallelogram with four right angles.

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Trapezoid Definition

A quadrilateral with only one pair of parallel sides.

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Square Definition

A parallelogram with four congruent sides and four right angles.

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Perimeter Definition

The distance around a two-dimensional shape.

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Kite Definition

A quadrilateral with two pairs of adjacent, congruent sides.

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Proportion Definition

A statement that two ratios are equal.

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Cross Multiplication

If a/b = c/d, then ad = bc.

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Similar Figures

Figures having the same shape but potentially different sizes.

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Similar Triangles

Corresponding angles are equal, corresponding sides are in proportion.

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AA Similarity

Triangles with same angle measures.

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SAS Similarity

Side-Angle-Side.

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SSS Similarity

Side-Side-Side.

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Right Triangle Altitude Theorem

In a right triangle, the altitude from the right angle to the hypotenuse divides the triangle into two triangles that are similar to the original triangle and to each other.

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Hypotenuse Definition

The longest side of a right triangle, opposite the right angle.

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Legs of a Right Triangle

The sides that form the right angle in a right triangle.

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Pythagorean Theorem

a² + b² = c², where a and b are legs and c is the hypotenuse.

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Angle of Elevation

An angle formed by a horizontal line and the line of sight to an object above the horizontal line.

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Angle of Depression

An angle formed by a horizontal line and the line of sight to an object below the horizontal line.

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Rhombus Diagonals

Diagonals of a rhombus intersect at 90 degrees.

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Rectangle Diagonal Property

Diagonals of a rectangle are equal in length.

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Square Diagonal Properties

Diagonals of a square bisect each other at right angles.

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Proportional Side Lengths

In similar triangles, corresponding sides are proportional.

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Scale Factor Definition

The ratio between two corresponding lengths in similar geometric figures.

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Study Notes

  • A closed plane figure with four sides is called a quadrilateral
  • A trapezoid is NOT a parallelogram
  • In a parallelogram, opposite angles are supplementary
  • Parallelograms are always quadrilaterals
  • Opposite sides of a parallelogram are always parallel
  • Diagonals of a parallelogram always intersect at a point
  • If angle SRQ supplements a 135° angle, then the meaure of angle SRQ is 45°
  • If one angle in parallelogram WXUV is 80°, then the measure of angle WVU, which is supplementary, is 100°
  • In rhombus ABCD, diagonals AC and BD intersect at E
  • If AE = 12, then AC, which is twice the length of AE, measures 24
  • Angle AED in rhombus ABCD, where the diagonals intersect, is 90°
  • In parallelogram GRAM, if angle G = 5x + 15 and angle R = 17x – 11, then the measure of angle G equals 65°
  • If AB is twice the length of AD, and AD measures 10 cm, the length of AB is 20 cm
  • For square MATH, all the sides are equal, therefore MA=AT=MT, and each angle equals to 90°
  • Given rhombus ABCD, if AB = (2x – 1) cm and CD = (x + 8) cm, then the length of AB is 17 cm
  • In rectangle MATH, with diagonals MT and AH meeting at S, segment MA is congruent to segment TH
  • Given rectangle LOVE with diagonals LV and OE meeting at S, LO equals VE
  • In rhombus GIFT, if angle GIF = 112°, then angle IFT equals 68°
  • In rhombus GIFT, if angle 3 = 33°, then angle 2 equals 57°
  • Diagonals intersect each other
  • Consecutive angles are supplementary
  • Opposite sides are congruent
  • Given a figure to find the value of x, x=4
  • Equality of two ratios is Proportion
  • Property of proportion demonstrating cross multiplication is: If w/x = y/z, then wz = xy

Finding Unknown Lengths and Sides Using Proportions and Similarity

  • The distance across the lake in the diagram is 13 mi
  • A quadrilateral with only one pair of parallel sides is a trapezoid
  • For the trapezoid with bases measuring 2 meters and 6 meters, the length of the median of the trapezoid is 4 meters
  • In kite PLAY : m∠A = 95°
  • For kite RSTV : RS = 8 cm, and ST = 12 cm
  • The perimeter of RSTV is 40 cm
  • Mr. Smith's garden (4 equal sides, 2 pairs of parallel sides and no angles in the corner) is a rhombus
  • In square RSTU, diagonals intersect at V, therefore m∠SRV = 45°
  • If parallelogram ABCD has a perimeter of and the length of side AB is 9, then the length of BC is 6 units
  • If HATS is a kite with diagonals intersecting at C, and measures 32°, then measure<SHC is 58°
  • Then is the equality of two ratios

Properties of Proportions

  • If W/X = Y/Z then, wz = xy
  • If the ratio of boys to girls in a classroom is 6 to 5, and there are a total of 48 boys in the classroom, then the ratio of the classroom is 6:5 = 48 : x
  • Given the proportion u/x = v/y then it leads to the equation uy = vx

Similar Triangles

  • Two triangles are congruent when triangles A and D are
  • The similarity concept justifies the answer, which is SAS Similarity Theorem
  • It is the longest side a right triangles
  • Use the figure and triangle to find the right measurements
  • Using the figure on the right, you should be able to establish measurements
  • Given the figure, refer to the angle of the elevation

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Mathematics 9 Summative Test PDF Exam Paper

Description

Test your knowledge of quadrilaterals! This quiz covers trapezoids, parallelograms, and rhombuses. Review the properties of each shape, including angles, sides, and diagonals.

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