6th Grade - Draw Quadrilaterals And Triangles

 
     
 
     
 
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6th
Geometry
Draw Quadrilaterals and Triangles
Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).
Know that triangles are figures with 3 sides and 3 angles. Classify Triangles by their sides and angles. When classifying a triangle by its sides use the terms equilateral, isosceles and scalene. The terms used to classify a triangle by its angles are right, acute, or obtuse. Any given triangle can be described using a combination of terms, one for the angle and one for the sides. Know that quadrilaterals are polygons with 4 angles and 4 sides. Classify quadrilaterals and give the most exact name for a quadrilateral by considering the sides and angles. The overall, general classification of a four-sided figure is called a quadrilateral. Any figure with four sides and four angles is considered a quadrilateral. Understand that quadrilaterals can be classified and named more specifically as a: parallelogram, rectangle, square, rhombus, or trapezoid.
 

Sample Problems

(1)

Draw a triangle with a 3 inch side between two angles that measure 30° and 60°. Then classify the triangle by its angles and its sides.

(right, scalene)

(2)

Classify the triangle according to its sides and angles.

(acute, equilateral)

(3)

Draw a quadrilateral with all four sides measuring 5 cm and two opposite angles measuring 130°. Then classify the quadrilateral with the most exact name.

(parallelogram)

(4)

Classify the quadrilateral in as many ways possible. Underline the most exact name.

(quadrilateral, parallelogram, rhombus)

(5)

A quadrilateral has three angles measuring 110, 100 and 80. What is the fourth angle measure? Then use a protractor to draw the quadrilateral and classify it, using the most exact name.

(70, quadrilateral)

Learning Tips

(1)

It is important to understand that the sum of angle measures for triangles and quadrilaterals are a constant. The sum of all angles of a triangle will always be 180°, where the sum of the measure of all angles in a quadrilateral will be 360°. You can use this information to find the missing angle of a triangle or quadrilateral and also when drawing either of these figures. A protractor can be used to construct an angle. This must be done when drawing a figure with specific angle measures. For example, if you are asked to draw a triangle with one 90° angle and 30° angle. You will need to use a protractor to draw both angles. After your angles are drawn you can use a ruler to connect the third line to make your triangle. You can use your protractor to measure the last angle that was created when you connect the last side and you will see that it is 60°.

(2)

Triangles are polygons with 3 sides and 3 corners. In fact, the word root tri- means three. Triangles can be classified in two ways. You may classify them by looking at their angles or by observing their sides. If you are looking at the angles, the triangles will be classified as acute, right or obtuse. Here are the attributes of each triangle when classifying by angle type.

An acute triangle has all angles that are acute, or less than 90 degrees.

A right triangle has one angle that is a right angle or exactly 90 degrees.

An obtuse triangle has one obtuse angle, greater than 90 degrees.

The second way that you may classify a triangle is by its sides. If you are looking at its sides, the triangle can be identified as equilateral, isosceles or scalene. Here is a brief definition and picture of each.

An equilateral triangle has all 3 sides congruent (the same size).

An isosceles triangle has at least two congruent sides.

A scalene triangle has no congruent sides. In other words all three sides have a different measure.

(3)

Quadrilaterals are polygons with four sides and four corners or angles. The word root quad- has the meaning of four. The quadrilateral family has several different names for each type of quadrilateral. However, quadrilaterals can be broken down into two categories: parallelograms or trapezoids. A trapezoid does not have any related figures. It can simply be called a trapezoid, as an exact name or a quadrilateral. The second category is parallelograms. There are several subtypes of parallelograms. In fact, the square, rectangle and rhombus can all also be classified as a parallelogram. Hence, all quadrilaterals have at lease two ways to be classified. However, some will have more. For example, the square can be classified as a rectangle, a rhombus, a parallelogram, a quadrilateral, or the most exact name, a square. The description below can be used to find the most exact name for a quadrilateral.

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

A rhombus is a parallelogram that has all sides congruent.

A rectangle is a parallelogram with four right angles.

A square is a rectangle, rhombus and parallelogram with all sides congruent. Looking at the descriptions above, we can understand why a square has so many names. A square is a quadrilateral because it has four sides and four corners. A square can also be classified as a parallelogram because both pairs of its opposite sides are parallel. A square can be classified as a rhombus because it is a parallelogram with all sides congruent. Finally, a square can be classified as a rectangle because it is a parallelogram with four right angles.

Though quadrilaterals can be classified in many ways, it is best to always label a quadrilateral with its most exact name, unless asked to do otherwise.


(4)

In order to draw triangles and quadrilaterals with specific angles, you will need a ruler and a protractor. A protractor can be used to draw specific angle sizes. A ruler can be used to draw the sizes the correct size. For the directions on how to used a protractor to make angles, click on the link: http://www.mathsisfun.com/geometry/protractor-using.html

(5)

You may want to use grid paper to construct angles. This will help keep your lines straight. If you get centimeter grid paper, you will be able to easily construct specified centimeter lengths. For example, if you wanted to draw a square with sides measuring 5 centimeters, you would start at the left edge of one square on the grid and count over 5 squares, because each square is worth one square centimeter.

Extra Help Problems

(1)

Draw a scalene triangle, with sides measuring 4 cm, 5 cm and 6 cm.

(The drawing should have all sides different measures, any angle size will do.)

(2)

Draw an equilateral triangle with all sides measuring 3 cm.

(The drawing must have all sides measuring exactly 3 cm.)

(3)

Draw an isosceles triangle with two sides measuring 5 cm and one side measuring 7 cm.

(The drawing must have two congruent sides and one longer side.)

(4)

Use a protractor to draw an acute triangle.

(Answers will vary: The angle must be 89 degrees or less.)

(5)

Use a protractor to draw a right triangle.

(Drawings will vary, the triangle must have exactly one 90 degree angle.)

(6)

Use a protractor to draw an obtuse triangle with one angle measuring 140°.

(Drawings will vary: exactly one angle must measure 140 degrees.)

(7)

Draw a triangle with a 5 cm side between two angles that measure 55° and 45°. Then classify the triangle by its angles and sides.

(acute, scalene)

(8)

Draw a triangle with all sides 4 cm and all angles 60º. Then classify the triangle by its angles and sides.

(acute, equilateral)

(9)

Draw a triangle with a 30º and 120º angle and two sides measuring 6 cm. Then classify the triangle by its angles and sides.

(obtuse, isosceles)

(10)

Draw a triangle with sides measuring 2 in., 1 ½ inches and 3 inches and angles measuring 58º, 47º and n. Find the value of n and then classify the triangle by its angles and sides.

(acute, scalene, n = 75)

(11)

Draw a triangle with a 120º angle, an 30º angle and the last angle measuring x. Find the value of x and then classify the triangle by its angles.

(x = 30º, obtuse)

(12)

Draw a triangle with a 90º angle, a 45º angle. Find the measure of the third angle. Measure the sides. Then classify the triangle by its angles.

(45º, right)

(13)

Draw square with 4 inch sides.

(Drawing should have four right, 90º angles and each side must measure 4 inches.)

(14)

Draw a trapezoid with two opposite sides measuring 3 cm. Next, draw sides worth 5 cm and 2 cm.

(The shape of the trapezoid can differ, but all sides must have the correct measures.)

(15)

Draw a parallelogram with opposite angles measuring 60º and 120º.

(Drawing must have opposite sides that are parallel and catty corner angles that have the same measure.)

(16)

Draw a rhombus with opposite angles measuring 80º and 70º and all sides measuring 4 cm.

(Drawing must not have any 90º angles. The angles are slightly smaller than a square. This is a diamond like shape.)

(17)

Draw a rectangle with opposite sides measuring 2 cm and 4 cm.

(Drawing must have 4 right angles and opposite sides with the same measure.)

(18)

Draw a quadrilateral with four sides measuring 4 cm and opposite angles measuring 100º and 80º. Then classify the quadrilateral with the most exact name.

(parallelogram)

(19)

Draw a quadrilateral with four 90º angles and four sides measuring 5 cm. Then list all classifications for the quadrilateral. Underline the most exact name.

(quadrilateral, parallelogram, rhombus, rectangle, and square)

(20)

Draw a quadrilateral with opposite sides measuring 6 cm and 10 cm and angles measuring 90º. Then list all classifications for the quadrilateral. Underline the most exact name.

(quadrilateral, parallelogram, rhombus, and rectangle)

(21)

Draw a quadrilateral with angles measuring 80º, 85°, 40° and x°. Find the measure of x. Then classify the quadrilateral.

(x = 150, quadrilateral)

(22)

Draw a 6 cm line segment with a 40º angle at one end and a 130º at the other end. Finally connect the two sides. Classify the quadrilateral with the most exact name.

(trapezoid)

(23)

Draw the quadrilateral and label all sides and angle measures. Four sides = 5 cm, Two opposite angles = 120°. Classify the figure with the most exact name.

(rhombus)

(24)

Draw the quadrilateral and label all sides and angle measures. The quadrilateral has congruent opposite sides at 8 cm and 2 cm, top right angles. Classify the figure.

(rectangle)

(25)

A quadrilateral has four congruent sides. One of its angles measures 77°. What are the measures of its other three angles.

(77, 103, 103)

 

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