# Properties of Triangles

- Posted by Brian Stocker
- Date Published February 26, 2019
- Date modified January 9, 2020
- Comments 0 comment

### Triangles – Example questions with step-by-step solution and explanation

Includes

- supplementary and complementary angles
- Proportion
- 30-60-90 and 45-45-90 Triangles
- Isosceles triangles
- Properties of Quadrilaterals

### Interior Angles (easy):

The interior angles of a triangle are given as 2x + 5, 6x and 3x – 23. Find the supplementary of the largest angle.

**Solution:**The interior angles of a triangle sum up to : 180^{0}(2x + 5) + (6x) + (3x – 23) = 18011x – 18 = 18011x = 198x = 18^{0}The largest angle is 6x = 6 . 18 = 108^{0}

The supplementary of an angle is the angle which added to 108^{0} gives 180^{0}. Then, the supplementary of is:180 – 108 = 72^{0}

The correct answer is (B).

### Proportion using Similarity Ratio (more difficult)

In the above triangle, AB // EC; |DE| = 3 cm, |EA| = 5 cm. Find the proportion of areas A(DEC) / A(ABCE).

A) 9/64

B) 9/55

C) 3/25

D) 3/5

**Solution:**

The triangles DEC and DAB are similar since AB is parallel to EC. Then, we have the similarity ratio:

|DE| / |DA| = 3/(3 + 5) = 3/8

The area of a triangle is found by base * height / 2. The similarity ratio 3/8 is valid for both the heights and bases of triangles DEC and DAB. This means that, the proportion of areas of DEC and DAB is the square of the similarity ratio:

A(DEC) / A(DAB) = (3/8)2 = 9/64

A(ABCE) = A(DAB) – A(DEC)

Then;

A(DEC) / A(ABCE) = 9 / (64 – 9) = 9/55

The correct answer is (B).

### Properties of 30-60-90 and 45-45-90 Triangles (easy)

Find the height of an equilateral triangle with side length of 6 cm.

**Solution:**

**The correct answer is (C).**

### Properties of 30-60-90 and 45-45-90 Triangles (more difficult)

**The correct answer is (B).**

### Properties of quadrilaterals (easy)

The diagonals of a rhombus are 6 cm and 8 cm. What is the perimeter of the rhombus equal to?

A) 16 cm

B) 18 cm

C) 20 cm

D) 24 cm

**Solution:** The diagonals of a rhombus intersect perpendicularly and bisect each other as shown below:

**The correct answer is (C).**

### Properties of Quadrilaterals (more difficult)

**The correct answer is (C).**

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

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