Mathematics 9: Quadrilaterals and Geometry
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Questions and Answers

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

  • Hexagon
  • Triangle
  • Pentagon
  • Quadrilateral (correct)

Which of the following quadrilaterals is NOT a parallelogram?

  • Rhombus
  • Rectangle
  • Square
  • Trapezoid (correct)

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

  • Parallelogram (correct)
  • Parallelogram (correct)
  • Parallelogram (correct)
  • Parallelogram (correct)

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

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

WXUV is a parallelogram, what is m WVU?

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

For numbers 8 9, refer to the figure on the right. ABCD is a rhombus. Diagonals AC and BD intersect each other at E. If AE = 12, what is AC?

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

What is m AED?

<p>90 (B)</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 (B)</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 (A)</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 (B)</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 (B)</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 (C)</p> Signup and view all the answers

For numbers 16-17, refer to rhombus GIFT. If mGIF = 112, then what is mIFT?

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

If m3 = 33, what is the m2?

<p>57 (C)</p> Signup and view all the answers

Which of the statements is NOT true about a square?

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

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

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

What is the value of x?

<p>34 (D)</p> Signup and view all the answers

Find the distance across the lake in the diagram.

<p>13 mi (D)</p> Signup and view all the answers

A quadrilateral with exactly one pair of parallel sides.

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

A cross section of a water trough is in the shape of a trapezoid with bases measuring 2 meters and 6 meters. What is the length of the median of the trapezoid?

<p>4 meters (D)</p> Signup and view all the answers

PLAY is a kite. What is mA?

<p>95 (D)</p> Signup and view all the answers

RSTV is a kite. If RS = 8 and ST = 12. What is the perimeter of kite RSTV?

<p>40 (A)</p> Signup and view all the answers

Mr. Smith's garden has 4 equal sides. It has 2 pairs of parallel sides. There are no right angles. What is the most precise name for the shape of Mr. Smith's garden?

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

RSTU is a square. The diagonals intersect at V. What is mSRV?

<p>45 because diagonals of a square bisect the angles (B)</p> Signup and view all the answers

The perimeter of the parallelogram ABCD is 30 units and the length of the side AB is 9 units, what is the length of BC?

<p>6 units (D)</p> Signup and view all the answers

Refer to the figure at the right, what is the value of x if the perimeter is equal to 93cm?

<p>9 cm (D)</p> Signup and view all the answers

HATS is a kite with diagonals that intersect at C. mTSC = 32, what is mSHC?

<p>58 (A)</p> Signup and view all the answers

It is the equality of two ratios.

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

Which of the following properties of proportion demonstrates cross multiplication?

<p>W/X = Z/Y then WZ = XY (C)</p> Signup and view all the answers

The ratio of number of boys to girls in a classroom is 6 to 5. If there are a total of 48 boys in the classroom, find the number of girls in the classroom. Which of the following best describes the problem?

<p>6:5 = 48 : x (A)</p> Signup and view all the answers

Which proportion leads to the equation uy = vx?

<p>Triangles C and D (B)</p> Signup and view all the answers

What similarity concept justifies your answer?

<p>SAS Similarity Theorem (D)</p> Signup and view all the answers

What is the value of x in 4/x = 1/14?

<p>56 (B)</p> Signup and view all the answers

The length of the shadow of your 15 meter height is 24 meters at a certain time in the morning. How high is a tree in your backyard if the length of its shadow is 16 meters?

<p>10 m (D)</p> Signup and view all the answers

Which proportion is correct according to the diagram?

<p>ST/OT = VW/OW (B)</p> Signup and view all the answers

If AE = 12, what is AC?

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

If mGIF = 112, then what is mIFT?

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

What is the value of x in $\frac{4}{x} = \frac{1}{14}$ ?

<p>56 (D)</p> Signup and view all the answers

Which proportion is correct?

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

Which two triangles are congruent?

<p>Triangles A and B (C)</p> Signup and view all the answers

Given: KLM ~ ABC. Find the value of x.

<p>15 (B)</p> Signup and view all the answers

In the figure, which triangle is congruent to ABIG?

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

Given: FR || ME. What is true about the similar triangles FAR and MAE?

<p>mR = mE (A)</p> Signup and view all the answers

Refer to ASPY and AIRK. What are the proportional corresponding side lengths?

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

Given that KS = 16 and SY = 4, which proportion is NOT correct?

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

What is the length of the hypotenuse if the legs of a right triangle measure 10 cm and 24 cm?

<p>26 cm (C)</p> Signup and view all the answers

ETG is similar to

<p>AGTE (B), AGTE (C)</p> Signup and view all the answers

What is the longest side of a right triangle?

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

If one of the legs a right triangle is 5 and the longest side is 13, what is the length of the other leg?

<p>12 (C)</p> Signup and view all the answers

Using the figure on the right, what kind of angle is being described by 40?

<p>Angle of Depression (C)</p> Signup and view all the answers

Given the figure on the right, which refers to the angle of elevation?

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

Flashcards

Quadrilateral

A closed, two-dimensional shape with four straight sides.

Parallelogram

A quadrilateral with two pairs of parallel sides.

Trapezoid

A quadrilateral with only one pair of parallel sides.

Parallelogram Opposite Angles

Opposite angles in a parallelogram are equal in measure.

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Rhombus

A parallelogram with four congruent (equal length) sides.

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Rhombus Diagonals

The diagonals of a rhombus bisect each other at right angles.

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Rectangle

A parallelogram with four right angles.

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Square

A quadrilateral with four congruent sides and four right angles.

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Consecutive Sides

Sides next to each other in a polygon. In a square all sides are same length.

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Kite

A quadrilateral with two pairs of adjacent sides congruent and no parallel sides.

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Square Diagonals Intersection

Point where the diagonals of a square intersect.

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Proportion

An equation stating that two ratios are equal.

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Cross Multiplication

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

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Similar Triangles

Triangles that have the same shape but may be different sizes.

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AA Similarity

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

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SSS Similarity

If all three pairs of corresponding sides are proportional, then the triangles are similar.

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Scale Factor

The ratio of corresponding sides of similar triangles.

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Triangle Proportionality Theorem

A line parallel to one side of a triangle divides the other two sides proportionally.

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Corresponding Angles (Similar Triangles)

In similar triangles, corresponding angles are congruent.

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Right Triangle Altitude Theorem

States that the altitude to the hypotenuse of a right triangle creates two smaller similar triangles.

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Hypotenuse

The side opposite the right angle in a right triangle.

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Legs of 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 above the horizontal line.

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Right Triangle

A right triangle consists of one 90 degree angle.

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Angle of Depression

An angle formed below the horizontal line.

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Adjacent side

The side adjacent (next to) to the angle.

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The opposite side

The side opposite to the angle.

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Complementary Angles

Angles that add up to 90 degrees.

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AA (Similarity)

Is when triangles share the same characteristics in their sides.

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Study Notes

  • This is a summative test for the third quarter in Mathematics 9, for SY 2024-2025.

Quadrilaterals

  • A closed plane figure consisting of four sides is called a quadrilateral.
  • A trapezoid is not a parallelogram.
  • Opposite angles in a parallelogram are supplementary.
  • Parallelograms are always quadrilaterals, and their opposite sides are always parallel.
  • Diagonals of a parallelogram always intersect at a point.
  • Diagonals bisect each other in a square.
  • Consecutive angles are supplementary in a square.
  • The opposite sides of a square are congruent.
  • Diagonals of a square are perpendicular.

Rhombus

  • In a rhombus, the diagonals AC and BD intersect each other at E.
  • If AE = 12, then AC = 24.
  • The measure of angle AED in a rhombus is 90 degrees.
  • If AB = (2x - 1) cm and CD = (x + 8) cm, then the length of AB is 17 cm.

Geometric Problems

  • If angle SRQ is supplementary to 135° then angle SRQ = 45 degrees
  • In parallelogram WXUV, if angle UVU is 80°, angle WVU is 100°.
  • If AB is twice the length of AD, and AD is 10 cm, then AB is 20 cm.
  • In square MATH, side MH is 27 cm.

Kites

  • PLAY is a kite, the measure of angle A is 64 degrees
  • RSTV is a kite with RS = 8 and ST = 12, its perimeter is 40.
  • With diagonals intersecting at C, and angle TSC being 32°, angle SHC = 58°. HATS is a kite

Proportions

  • The equality of two ratios is a proportion
  • Cross multiplication is demonstrated when a/b = x/y then ay = bx.
  • If the ratio of boys to girls is 6 to 5, and there are 48 boys, then 6:5 :: 48:x describes the problem to find girls (x).
  • The proportion that leads to the equation uy = vx is u/x = v/y.

Similarity and Congruence

  • SSS (Side-Side-Side) Similarity Theorem justifies similarity.
  • If FR || ME then angle R is congruent to angle E
  • Side lengths are proportional in similar triangles
  • Given a right triangle with legs 10 cm and 24 cm, the hypotenuse is 26 cm.
  • Triangle ETG is similar to triangle NTK

Angle of Elevation/Depression

  • An Angle of Elevation measures above a horizonal line

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Related Documents

Mathematics 9 Summative Test PDF Exam Paper

Description

This test covers quadrilaterals, parallelograms, squares, and rhombuses. It includes problems on angle measurements, side lengths, and properties of diagonals. This is for Math 9, Quarter 3.

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