geometry tests high school

a) Given an equation, to find the corresponding locus. b) Given a locus under some geometrical condition to determine the corresponding equation. The following properties of the curve will be very helpful in determining the full form of locus equation. i) Intercept: The intercept of a curve are th..

Introduction - Geometry originated when man felt the need to measure his land. Ancient Egyptians were perhaps the first people to study geometry. Later, the Babylonians studied in a systematic wa..

Question 1 - Question: Using Heron's formula find the area of an equilateral triangle whose perimeter is 15 cm. Answer: Perimeter = 15 cm Each side (a) = 5 ..

Question 1 - Question: Prove that the area of a trapezium is half the product of its height and the sum of the parallel sides. Answer: Given: ABCD is a trapezium in which AB || DC. Let AB = a, DC = b and CE = AF = h. To prove: Construction: Join AC. Proof: AC is the diagonal of quad. ABCD. area of ..

Question 1 - Question: If p is the length of perpendicular drawn from the origin on the line AB whose intercepts on the axes are a and b, then show Answe..

Question 1 - Question: Find the value of 'a' for which the lines ax + 4y + 5 = 0 and 9x + ay - 4 = 0 are parallel to each other. Answer: ax + 4y + 5 = 0 and 9x + ay - 4 = 0 are parallel to each other, the slopes are equa..

Question 21 - Question: Three angles of a quadrilateral are 100 o , 48 o and 92 o . Find the 4 t h angle. Answer: quadrilateral is 360 o ] =120 o The 4 t h angle measures 120 o..

Question 1 - Question: If the distance between the points (5, -6) and (x, -1) is 13, find the positive values of x. [3 Mark] Answer: The distance between two points is given by Given A (5, -6), B (x, -1), AB = 13 Squaring both the side..

Question 1 - Question: Prove that if a line be drawn Parallel to the base of a D , the portion intercepted by the sides is bisected by the median to the base. [3 Mark] Answer: Given: In D ABC, PQ||BC. AD is the median of BC and meets BC in D. To prove: PR = RQ R is midpoint of PQ. Proof: Since PQ||..