2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove that if the converse of the Alternate Interior Angle Theorem is true, then all triangles have zero defect. [Hint: For an arbitrary triangle, ABC, draw a line through C parallel to side AB. Justify why you can do this.]

Q: 2. In a quadrilateral ABCD, ZA = 72° and 2C is the supplementary of ZA. The other two angles are…

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Q: 4. State and prove synthetically the converse of the angle bisector theorem. B P E C

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Q: In the accompanying diagram, AB CD and intersects transversal GH at points E and F respectively.…

A: Consider the following figure: AB↔∥CD↔ GH↔ is transversal.

Q: Q3. Evaluate [(A +B). (à – B)] if à = 2î – 3ĵ + 5k and B = 3î + j – 2k

A: Topic:- algebra  Note:- as per our guideline if more than one question uploaded than only one…

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

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Q: Which of the following could NOT be used to prove that MNOP is a rectangle? O MP=NO and MN=PO Both…

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Q: Wouldn't that be 9x-7? Why is it +7?

A: No. The explanation is given below

Q: 7. In which triangle do the three perpendicular bisectors intersect outside the triangle? 1) a right…

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Q: 2. (a) Explain what it means to say that two triangles are similar. (b) State a condition for two…

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Q: State and prove the converse of the corresponding angles theorem.

A: State and prove the converse of the corresponding angles theorem.

Q: 4x-2y+2z=4.   (a)  Compute the angle between these planes. (b)  Compute the line of intersection…

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Q: Z1 and 2 are supplementary. If two angles are supplementary, then the sum of their measures is 180.

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Q: Given points P(5, 2, -1), Q(2, -3, 0), T(4, 2, 4) foms the triangle. Find the interior angle at Q

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Q: 4. AB intersects CD at E. If the mLAEC is 8x- 15 and mLAED is 9x + 76, find all the angles.

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Q: Use the converse of Ceva’s theorem to prove that the angle bisectors of the interior angles of a…

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Q: paralle M = be on planes Q and R respectively. A clear writing is expected.) (a) Why are the lines L…

A: Given, two pararllel planes Q and R. Let the lines                   L=1-2t, 4+t, 3 and M=5t, 1-t,…

Q: 1. State and prove the full version of the Pythagorean Theorem

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Q: A is a point on the y-axis such that AB // DC. Given points A(0,a), B(3,3), C(11,9), and D(8,13)...…

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Q: Find: a. Vertex b. focal width c. End points of the lactus rectum

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Q: 2. It is possible for two angles of a triangle in the hyperbolic plane to each have a measure of 2.

A: Solution

Q: irectly opposite on the other side/shore. If the speed of the boat (in still water) is 16 mph and he…

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Q: Calculate the distance of AB. A. (-2,8) B (5,3)

A: Here, we need to find distance between two points A(-2, 8) and B(5, 3). We know that the distance…

Q: 3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The corners…

A: a)Co-ordinates of GG0+7.52,0+02,0+02=G154,0,0Co-ordinates of P∵P lies on the  xy planeso…

Q: (4) Prove that if two altitudes in a triangle are congruent, then the triangle is Isosceles.

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Q: AB²+ AC² = 2(AO² + BO²) e O is the middle point of BC.

A: Part A