Properties of Triangles

Includes

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

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 : 180⁰(2x + 5) + (6x) + (3x – 23) = 18011x – 18 = 18011x = 198x = 18⁰The largest angle is 6x = 6 . 18 = 108⁰

The supplementary of an angle is the angle which added to 108⁰ gives 180⁰. Then, the supplementary of is:180 – 108 = 72⁰

The correct answer is (B).

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 (A).

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

Solution:

The correct answer is (C).

The correct answer is (B).

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).

The correct answer is (C).