**Ordering Triangle Sides and Angles Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on ordering triangle sides and angles.

Before look at the worksheet, if you would like to know the stuff related to ordering triangle sides and angles,

**Problem 1 : **

List the sides of the triangle from shortest to longest.

**Problem 2 :**

List the angles of the triangle from smallest to largest.

**Problem 3 :**

Given the lengths of the three sides in a triangle, list the angles in order from smallest to largest.

side XY = 13 units

side YZ = 10 units

side XZ = 7 units

**Problem 4 :**

In triangle ABC, we have

∠A = x^{o}, ∠B = (2x - 20)^{o }and ∠C = (3x - 22)^{o}

List the sides of the triangle from longest to shortest.

**Problem 1 : **

List the sides of the triangle from shortest to longest.

**Answer :**

In any triangle, the smallest angle is always across from the shortest side and the largest angle is always across from the longest side.

In the triangle ABC given above , because angle C is the smallest angle, the side AB must be the shortest side.

And also, because angle B is the largest angle, the side AC must be the longest side.

Let's put all together.

Hence, the order of the three sides from shortest to longest is

side AB, side BC and side AC

**Problem 2 :**

List the angles of the triangle from smallest to largest.

**Answer :**

In any triangle, the shortest side is always across from the smallest angle and the longest side is always across from the largest side.

In the triangle PQR given above , because the side QR is the shortest side, the angle P must be the smallest angle.

And also, because the side PQ is the longest side, the angle R must be the largest angle.

Let's put all together.

Hence, the order of the three angles from smallest to largest is

angle P, angle Q, and angle R

**Problem 3 :**

Given the lengths of the three sides in a triangle, list the angles in order from smallest to largest.

side XY = 13 units

side YZ = 10 units

side XZ = 7 units

**Answer : **

Let us sketch the triangle XYZ with

XY = 13, YZ^{ }= 10^{ }and XZ = 7

In any triangle, the shortest side is always across from the smallest angle and the longest side is always across from the largest side.

In the triangle XYZ given above , because the side XZ is the shortest side, the angle Y must be the smallest angle.

And also, because the side XY is the longest side, the angle Z must be the largest angle.

Let's put all together.

Hence, the order of the three angles from smallest to largest is

angle Y, angle X, and angle Z

**Problem 4 :**

In triangle ABC, we have

∠A = x^{o}, ∠B = (2x - 20)^{o }and ∠C = (3x - 22)^{o}

List the sides of the triangle from longest to shortest.

**Answer : **

By triangle sum theorem,

Sum of the three angles in a triangle = 180^{o}

So, we have

∠A + ∠B + ∠C = 180^{o}

x^{o }+ (2x - 20)^{o }+ (3x - 22)^{o }= 180^{o}

x + 2x - 20 + 3x - 22 = 180

Simplify.

6x - 42 = 180

Add 42 on both sides.

6x = 222

Divide both sides by 6.

x = 37

Then, we have

∠A = x^{o }= 37^{o}

∠B = (3 ⋅ 37 - 22)^{o }= 89^{o}

∠C = (2 ⋅ 37 - 20)^{o }= 54^{o}

Let us sketch the triangle ABC with

∠A = 37^{o, }∠B^{ }= 89^{o }and ∠C = 54^{o}

In any triangle, the largest angle is always across from the longest side and also the smallest angle is always across from the shortest side .

In the triangle ABC given above , because angle B is the largest angle, the side AC must be the longest side.

And also, because angle A is the smallest angle, the side BC must be the shortest side.

Let's put all together.

Hence, the order of the three sides from longest to shortest is

side AC, side AB and side BC

After having gone through the stuff above, we hope that the students would have understood how to order the sides and angles of a triangle from least to greatest.

Apart from the stuff given on "Ordering triangle sides and angles worksheet", if you need any other stuff, please use our google custom search here.

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