# Properties of Triangles

- Posted by Brian Stocker
- Date Published February 26, 2019
- Date modified May 28, 2019
- 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.

Next post

##### Real world problems with ratio, proportion, direct, inverse and joint variations

### You may also like

##### Study Tips and Methods to try

Study Tips and Methods to try Everyone absorbs information in different ways. See our guide to learning styles and learning styles quiz. Study and conduct self-tests At this stage your aim is not to just keep rereading the material. This …