Grade 5 Geometry. Answer the questions. For more such worksheets visit

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ID : ae-5-geometry [1] Grade 5 Geometry For more such worksheets visit www.edugain.

1 ID : ae-5-geometry [1] Grade 5 Geometry For more such worksheets visit Answer the questions (1) A 4-sided flat shape with straight sides where the opposite sides are parallel is called a. (2) Identify the points that lie in the exterior of the circle. A B F D C E (3) In a triangle, the second angle is one third of the first angle, and the first angle is 1.5 times the third angle. What is the value of the third angle? (4) If BDC and ACB are right angles, find the value of CBD. (5) Are AG and BE intersecting? (6) How many rays can be drawn from a given point? (7) What term can be used to describe the angles of a regular pentagon? (8) An angle whose measure is 180 is called a/an. (9) In a triangle, one angle is a complement of the other angle. What is the value of the third angle?

2 (10) Find the measure of BAC. ID : ae-5-geometry [2] (11) Identify the semicircle that contains 'C'. A O B C Choose correct answer(s) from the given choices (12) Two lines that are not parallel will meet. a. most of the times b. never c. sometimes d. always (13) Study the following: M: Sum of the lengths of any two sides of a triangle. N: Third side of the same triangle. Which of the given relations is true with respect to a triangle? a. M = N b. M and N are not related c. M > N d. M < N (14) The points which lie on a straight line are called points. a. non-collinear b. collinear Check True/False (15) The length of a ray or a line can not be measured. True False

ID : ae-5-geometry [3] 2017 Edugain (www.edugain.com).

4 Answers ID : ae-5-geometry [4] (1) Parallelogram Remember: A four-sided flat shape where the opposite sides are parallel is called a parallelogram. Here, AB DC and BC AD. (2) D, E, and F The points that lie outside the circle are said to lie in the exterior of the circle. We can see that the points D, E, and F lie outside the circle, hence they are located in the exterior of the circle.

5 (3) 60 ID : ae-5-geometry [5] It is given that the second angle is one third of the first angle. Therefore, the sum of the second and the first angle will be (1+1/3) times the first angle... (Statement 1) It is also given that the first angle is 1.5 times the third angle. In other words, the third angle is two third of the first angle... (Statement 2) Step 3 By combining the statements 1 and 2, we can say that: Sum of all three angles is double of the first angle. Step 4 We also know that the sum of all angles of a triangle is 180. Step 5 Since double of the first angle is 180, the first angle should be 90. Step 6 Since third angle is two third of first angle, third angle = 60 (In higher grades you will learn Algebra, using which such questions can be solved very easily. For more details read this article. Algebra A fascinating subject) (4) 60 We know that the sum of all the interior angles of a triangle is 180. Therefore, for triangle ΔABC, CBD + BCA + CAD = 180 CBD = 180 CBD = ( ) CBD = 60

6 (5) No ID : ae-5-geometry [6] We know that the intersecting lines are the lines that meet at a point. Also, we can see that the two given lines are equidistant from each other at all the points. Hence, they will never meet. So, the lines AG and BE are not intersecting. (6) Infinite We know that a ray is a line segment that extends endlessly in one direction. Let us try to draw the rays starting from a given point. Step 3 Observe the light rays emerging from the sun. We see that infinite light rays emerge from a single point(sun) in all the directions. Step 4 We can see that infinite rays can be drawn through a given point.

7 (7) obtuse angle ID : ae-5-geometry [7] Let us first find the measure of each angle in a regular pentagon. We know that in a polygon with n sides, the sum of all its internal angles is 180 (n - 2). Since, a pentagon is a polygon with five sides, the sum of all the internal angles of a pentagon is 180 (5-2) = = 540. Step 3 In a regular pentagon, all the internal angles are equal. Thus, the measure of each internal angle = 540 = (The following figure shows a regular pentagon) Step 4 We know that an obtuse angle is an angle whose measure is more than 90 but less than 180. Step 5 Hence, the term that can be used to describe the angles of a regular pentagon is obtuse angle.

8 (8) straight angle ID : ae-5-geometry [8] The angle whose measure is 180 will look as: It is called a straight angle. (9) 90 Let us recall the fact that in a triangle, the sum of all its internal angles is 180. Let us look at the definition of complementary angles: two angles are complementary if their sum is 90. Step 3 In the given triangle, two angles are complementary to each other. This means, the sum of two angles is 90. Let us assume the third unknown angle is y. This means: y + 90 = 180 or, y = or, y = 90 Step 4 Therefore, the third angle is 90. (10) 60 Let us note the mark on the rim of the protractor through which arm AC passes. We see that the mark 0 lies on AB and AC passses through 60. Hence, the measure of BAC is 60.

9 (11) Semicircle ACB ID : ae-5-geometry [9] Remember: A half-circle formed by cutting a full circle along its diameter is called a semicircle. As AB is the diameter, the given circle is divided into semicircle ACB and semicircle AB. Step 3 We can see that the point 'C' lies in the semicircle ACB. (12) d. always Let us draw two lines that are not parallel. As shown in the above figure the two lines are not parallel. But they will intersect each other at some point when extended. Therefore, two lines will always meet if they are not parallel. (13) c. M > N Remember: If the sum of the lengths of any two sides of a triangle is greater than the third side, then a triangle can be formed. So, Sum of the lengths of any two sides of a triangle > Third side of the same triangle. M > N Hence, M > N is the correct relation about forming a triangle.

10 (14) b. collinear ID : ae-5-geometry [10] Let us draw the points that lie on a straight line. P Q R P, Q, and R are collinear points. The points which lie on a straight line are called collinear points. (15) True The length of a ray or a line cannot be measured because it does not have a definite length. A line segment which is extended endlessly in one direction becomes a ray. Similarly, a line segment that has been extended endlessly in both the directions becomes a line. A Ray A Line Thus, the correct answer is True.

Grade 5 Geometry. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

Grade 5 Geometry. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit ID : ae-5-geometry [1] Grade 5 Geometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) How many Line Segments can be drawn on a plane? (2) What is the sum of the angles that