Question

If ABCD is a convex quadrilateral prove that the diagonals (AC) and (BD) intersect

If ABCD is a convex quadrilateral prove that the diagonals (AC) and (BD) intersect

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In the rectangle ABCD, AB = 6 and BC = 8. The diagonals AC and BD...
In the rectangle ABCD, AB = 6 and BC = 8. The diagonals AC and BD intersect at O. Point P lies on the diagonal AC such that AP = 1. A line is drawn from B through P and meets AD at S. Let be R a point on AD such that OR is parallel to BS. a) Find the lengths of AS and RD. Hint: Denote AS = x. Use P S k OR and OR k BS...
Prove the following: Claim: Consider a convex quadrilateral □ABCD. If σ(□ABCD) = 360, then σ(▵ABC) =...
Prove the following: Claim: Consider a convex quadrilateral □ABCD. If σ(□ABCD) = 360, then σ(▵ABC) = σ(▵ACD) = 180. Hint: Use the Split Triangle Theorem and/or the Split Quadrilateral Theorem (The angle sum of a convex quadrilateral is the sum of the angle sum of the two triangles formed by adding a diagonal. Recall: The angle sum of quadrilateral □ABCD is σ(□ABCD) = m∠ABC + m∠BCD + m∠CDA + m ∠DAB.)
In a circle with center O, consider two distinct diameters: AC and BD. Prove that the...
In a circle with center O, consider two distinct diameters: AC and BD. Prove that the quadrilateral ABCD is a rectangle. Include a labeled diagram with your proof.
Let ABCD be a cyclic quadrilateral, and let the diagonals meet in point S. From S,...
Let ABCD be a cyclic quadrilateral, and let the diagonals meet in point S. From S, draw perpendiculars to the four sides, with feet L on AB, M on BC, N on CD and K on DA. This gives a new quadrilateral LM N K. Prove that the sum of two opposite angles in this new quadrilateral is double the corresponding angle at the intersection S. (E.g.∠L+∠N= 2∠ASB). Hint: Find four smaller cyclic quadrilaterals in the diagram.
Prove the conjecture that if a given quadrilateral ABCD and it’s angle bisectors form a new...
Prove the conjecture that if a given quadrilateral ABCD and it’s angle bisectors form a new quadrilateral WXYZ, then a circle can be constructed on the vertices of quadrilateral WXYZ.
Trapezoid ABCD has ∠BAD = ∠ADC = 90◦ , AB = x, and DC = y...
Trapezoid ABCD has ∠BAD = ∠ADC = 90◦ , AB = x, and DC = y with x < y. Diagonals AC and BD intersect at X. Point L is on AD and point M is on BC so that LM is parallel to AB and LM passes through X. Determine the length of LM in terms of x and y.
A parallelogram ABCD is called a rhombus if AB = BC = CD = DA. Suppose...
A parallelogram ABCD is called a rhombus if AB = BC = CD = DA. Suppose ABCD is a rhombus. Prove that AC is perpendicular to BD.
A kite is defined as a quadrilateral with two distinct pairs of adjacent sides equal. Prove...
A kite is defined as a quadrilateral with two distinct pairs of adjacent sides equal. Prove that in a kite the angles between the pairs of equal sides are equal and that the diagonals are perpendicular.
Consider a quadrilateral ABCD such that ∠BAD and ∠ADC are perpendicular, the rays AB and CD...
Consider a quadrilateral ABCD such that ∠BAD and ∠ADC are perpendicular, the rays AB and CD are on the same side of the line AD, and AB ≅ CD. Prove the following claims on E2, H2, and S2. ∠ABC ≅ ∠DCB. the perpendicular bisector of AD is also the perpendicular bisector of BC. Hint: Look for symmetries.
Consider a quadrilateral ABCD such that ∠BAD and ∠ADC are perpendicular, the rays AB and CD...
Consider a quadrilateral ABCD such that ∠BAD and ∠ADC are perpendicular, the rays AB and CD are on the same side of the line AD, and AB ≅ CD. Quadrilaterals with these properties are called Khayyam quadrilaterals Prove the following claims on E2, H2, and S2. ∠ABC ≅ ∠DCB. the perpendicular bisector of AD is also the perpendicular bisector of BC. Hint: Look for symmetries.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT