Green Bridge Learning Resource For Triangles And Polygons

Overview

Welcome to the Plane Geometry course material focusing on the fascinating and fundamental topic of Triangles and Polygons. In this comprehensive overview, we will delve into the intricate properties and relationships within triangles and polygons, aiming to understand their nature, angles, sides, and areas.

One of the primary objectives of this topic is to help you comprehend the properties of triangles and polygons. Triangles, which are three-sided polygons, hold various essential characteristics that distinguish them from other shapes. Understanding the angle sum properties of polygons will enable you to calculate the interior angles of different polygons efficiently.

As we explore triangles, it is crucial to distinguish between the different types such as scalene, isosceles, and equilateral triangles based on their sides and angles. Moreover, identifying congruent triangles, which are triangles that have the same size and shape, plays a key role in geometry and problem-solving.

Special triangles, including isosceles, equilateral, and right-angled triangles, exhibit unique properties that simplify calculations and proofs. For instance, the Pythagorean theorem is a famous result specific to right-angled triangles that relates the lengths of the sides.

Furthermore, we will delve into the properties of special quadrilaterals like parallelograms, rhombuses, squares, rectangles, and trapeziums. Each of these quadrilaterals has distinct attributes that make them valuable in geometry, such as the equal opposite angles in a parallelogram and the right angles in a rectangle.

Similar triangles, which have the same shape but not necessarily the same size, share proportional sides and equal corresponding angles. Understanding the properties of similar triangles is essential for applications in trigonometry, navigation, and architecture.

Exploring the relationships between angles and sides in polygons will enhance your problem-solving skills and geometric reasoning. The sum of the angles of a polygon formula ( (n - 2)180o or (2n – 4) right angles) provides a general method to calculate the total internal angles of any polygon.

Finally, the course material will cover the intriguing theorem of intercept (interior opposite angles are supplementary) and the relationship between exterior angles of polygons and their interior angles. These topics will deepen your knowledge of geometrical principles and applications.

Throughout this course material, we encourage you to engage actively with the content, practice applying the theorems and properties, and enjoy the beauty of geometric relationships in triangles and polygons.

Objectives

Distinguish between types of triangles and polygons
Calculate the areas of special triangles and quadrilaterals
Apply the angle sum properties of polygons
Apply the properties of similar triangles in problem-solving
Explore relationships between angles and sides in polygons
Use the properties of parallelograms and other special quadrilaterals
Identify congruent triangles
Understand the properties of triangles and polygons

Lesson Note

In geometry, triangles and polygons are fundamental shapes that are seen everywhere around us. From architectural designs to natural formations, understanding these shapes is crucial in both academics and practical scenarios. This lesson will delve into the various types of triangles and polygons, explore their properties, and learn how to calculate their areas.

Lesson Evaluation

Congratulations on completing the lesson on Triangles And Polygons. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

What is the sum of the interior angles of a triangle? A. 90 degrees B. 180 degrees C. 270 degrees D. 360 degrees Answer: B. 180 degrees
In a triangle, if one angle is 70 degrees and another angle is 50 degrees, what is the measure of the third angle? A. 35 degrees B. 60 degrees C. 70 degrees D. 80 degrees Answer: D. 80 degrees
If two angles of a triangle are 30 degrees and 60 degrees, what is the measure of the third angle? A. 60 degrees B. 70 degrees C. 80 degrees D. 90 degrees Answer: D. 90 degrees
In a quadrilateral, if one angle measures 120 degrees, what is the sum of the other three angles? A. 120 degrees B. 180 degrees C. 240 degrees D. 360 degrees Answer: D. 360 degrees
If the exterior angle of a triangle is 110 degrees, what is the sum of the two interior opposite angles? A. 110 degrees B. 140 degrees C. 180 degrees D. 360 degrees Answer: C. 180 degrees
In a parallelogram, what is the sum of the interior angles? A. 180 degrees B. 270 degrees C. 360 degrees D. 720 degrees Answer: C. 360 degrees
What are the properties of a rhombus? A. All sides equal, opposite sides parallel B. All angles equal C. Both A and B D. None of the above Answer: C. Both A and B
If a quadrilateral has one pair of parallel sides and one pair of equal sides, what type of quadrilateral is it? A. Rhombus B. Parallelogram C. Rectangle D. Trapezium Answer: D. Trapezium
If a triangle has angle measures of 30 degrees, 60 degrees, and 90 degrees, what type of triangle is it? A. Isosceles triangle B. Right-angled triangle C. Equilateral triangle D. Scalene triangle Answer: B. Right-angled triangle

Recommended Books

	Geometry Subtitle Understanding Shapes and Spaces Publisher Pearson Year 2017 ISBN 978-0134080210
	Mathematical Methods in the Physical Sciences Subtitle A Comprehensive Guide Publisher Wiley Year 2016 ISBN 978-1118471433

Past Questions

Wondering what past questions for this topic looks like? Here are a number of questions about Triangles And Polygons from previous years

WAEC SSCE - General Mathematics - 1997 (Click to take full assessment)

Question 1 Report

O is the centre of the circle PQRS. PR and QS intersect at T POR is a diameter, ?PQT = 42^o and ?QTR = 64^o; Find ?QRT

68^o

64^o

42^o

32^o

22^o.

View Answer

JAMB UTME - Mathematics - 2023 (Click to take full assessment)

Question 1 Report

PQRS is a cyclic quadrilateral. Find $x$ + $y$

Answer Details

∠PQR + ∠PSR = 180o (opp. angles of cyclic quad. are supplementary)

⇒ 5 $x$ - $y$ + 10 + (-2 $x$ + 3 $y$ + 145) = 180

⇒ 5 $x$ - $y$ + 10 - 2 $x$ + 3 $y$ + 145 = 180

⇒ 3 $x$ + 2 $y$ + 155 = 180

⇒ 3 $x$ + 2 $y$ = 180 - 155

⇒ 3 $x$ + 2 $y$ = 25 ----- (i)

∠QPS + ∠QRS = 180o (opp. angles of cyclic quad. are supplementary)

⇒ -4 $x$ - 7 $y$ + 150 + (2 $x$ + 8 $y$ + 105) = 180

⇒ -4 $x$ - 7 $y$ + 75 + 2 $x$ + 8 $y$ + 180 = 180

⇒ -2 $x$ + $y$ + 255 = 180

⇒ -2 $x$ + y = 180 - 255

⇒ -2 $x$ + $y$ = -75 ------- (ii)

⇒ $y$ = -75 + 2 $x$ -------- (iii)

Substitute (-75 + 2 $x$ ) for $y$ in equation (i)

⇒ 3 $x$ + 2(-75 + 2 $x$ ) = 25

⇒ 3 $x$ - 150 + 4 $x$ = 25

⇒ 7 $x$ = 25 + 150

⇒ 7 $x$ = 175

⇒ $x = \frac{175}{7} = 25$

From equation (iii)

⇒ $y$ = -75 + 2(25) = -75 + 50

⇒ $y$ = -25

∴ $x$ + $y$ = 25 + (-25) = 0

View Answer