# Constructing Triangles

#### Grade 7 Math Worksheets

**Constructing Triangles refers to the process of drawing a triangle with given measurements of its sides and/or angles.**

Table of Contents:

- Constructing Triangles
- Side-Side-Side (SSS) Method
- Side-Angle-Side (SAS) Method
- Angle-Side-Angle (ASA) Method
- Formula
- Solved Questions
- FAQs

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## Constructing Triangles - Grade 7 Math Worksheet PDF

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## Constructing Triangles

Constructing triangles refers to the process of drawing a triangle with given measurements of its sides and/or angles.

### There are three common methods for constructing triangles:

#### 1. Side-Side-Side (SSS) Method:

To construct a triangle using the SSS method, you need to draw three straight lines that represent the lengths of the three sides of the triangle. Then, you connect the endpoints of these lines to form a triangle.

#### 2. Side-Angle-Side (SAS) Method

**Step 1:** To construct a triangle using the SAS method, you need to draw two straight lines that represent the lengths of two sides of the triangle, and an angle between them

**Step 2:** Then, you draw a line from the endpoint of one of these sides to the opposite side, using the given angle as a reference.

**Step 3: **This line should intersect the opposite side at a point, and you can connect this point to the endpoints of the two given sides to form a triangle.

This will be more clear to the students.

#### 3. Angle-Side-Angle (ASA) Method

**Step 1:** Need to draw two angles and a side that connects them.

**Step 2:** Then, draw another angle that shares one of the sides with one of the given angles.

**Step 3:** Finally, connect the endpoints of the two sides that form this shared angle to form a triangle.

Note that not all combinations of measurements will produce a valid triangle. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side, and the sum of the angles in a triangle must be equal to 180 degrees.Example: If sides of the triangle are A, B, and C, then

1) A+B > C

2) B+C > A

3) C+A > B

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## Formulas

There are several formulas that can be used in the context of constructing triangles:

**Law of Cosines:** This formula can be used to find the length of a side of a triangle if the lengths of the other two sides and the angle between them are known. The formula is:

c^2 = a^2 + b^2 – 2ab cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

**Law of Sines:** This formula can be used to find the lengths of the other sides of a triangle if the length of one side and the angles opposite that side are known. The formula is:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides, and A, B, and C are the angles opposite those sides.

**Pythagorean Theorem:** This formula can be used to find the length of the third side of a right triangle if the lengths of the other two sides are known. The formula is:

a^2 + b^2 = c^2

where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.

These formulas are useful in a variety of applications, including the construction of triangles and other geometrical shapes.

## Solved Questions

Here are some solved questions related to constructing triangles using formulas:

Given a triangle with sides of length 5, 8, and 10, find the measure of angle C.

We can use the Law of Cosines to solve for angle C. Since side c has length 10 and sides a and b have lengths 5 and 8, respectively, we have:

10^2 = 5^2 + 8^2 – 2(5)(8)cos(C)

Simplifying, we get:

100 = 89 – 80cos(C)

11 = 80cos(C)

cos(C) = 11/80

Taking the inverse cosine, we find that:

C ≈ 83.1 degrees

So angle C has a measure of approximately 83.1 degrees.

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## Constructing Triangles FAQS

##### What are the necessary conditions for constructing a triangle?

To construct a triangle, we need to know the lengths of at least two sides and the measure of at least one angle. Alternatively, we can know the lengths of all three sides, or the lengths of one side and the measures of two angles.

##### Can any three lengths of sides form a triangle?

No, not any three lengths of sides can form a triangle. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem. If this condition is not satisfied, the three lengths cannot form the sides of a triangle.

##### How do we use the Law of Sines to construct a triangle?

The Law of Sines can be used to find the lengths of the other sides of a triangle if the length of one side and the angles opposite that side are known. To use the Law of Sines to construct a triangle, we first draw the given side and the angle opposite it. We then use the Law of Sines to find the ratios of the lengths of the other sides to the length of the given side. We can then use a compass and straightedge to construct the triangle using these ratios.

##### How do we use the Law of Cosines to construct a triangle?

The Law of Cosines can be used to find the length of a side of a triangle if the lengths of the other two sides and the angle between them are known. To use the Law of Cosines to construct a triangle, we first draw the two sides whose lengths are known and the angle between them. We then use the Law of Cosines to find the length of the third side. We can then use a compass and straightedge to construct the triangle using the lengths of the sides.

##### What are some common applications of triangle construction?

Triangle construction has many practical applications, such as in architecture, engineering, surveying, and navigation. For example, engineers may use triangle construction to design bridges or other structures, while surveyors may use it to measure the heights of buildings or mountains. In navigation, triangle construction is used to determine the location of a ship or plane based on the angles between certain landmarks.

**Gloria Mathew** writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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