Properties of Triangles
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 : 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).
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 (A).
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).
