middle school geometry


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Fundamental problems of Analytical Geometry
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..
Theorem 4
A perpendicular drawn from the right angle vertex of a right - angled triangle divides the triangle into two triangles similar to each other and also to the original triangle. ABC is a triangle right-angled at A. The perpendicular from A to BC meets BC at D. (i) (ii) (ii..
Question 3
Question: Answer: ( exterior angle = sum of int. opposite angle) ..
Question 10
Question: Answer: This is true if eithe..
Question 4
Question: Answer: ..
Proof:
(i) ( Theorem) From (i) and (ii), ..
Proof:
Now in triangles, ABD and ABC, AB=AB (common side) (each angle is a right angle) AD=BC (opposite sides of parallelogram) BD=AC (corresponding parts of corresponding triangles) Hence the theorem is prov..
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