Question

prove

in a saccheri quadrilateral, the length of the summit is greater than the length of the base

Answer #1

Corollary 6.1.10. In a Saccheri quadrilateral, the length of the
summit is greater than the length of the base.
please proof

Describe the Saccheri Quadrilateral and prove in neutral
geometry that the summit angles are congruent.

show that if the summit and the base angles of two saccheri
quadrilaterals are congruent then the reamining sides are
congruent.

If a quadrilateral has all sides of equal length and one angle
equal to 90◦, prove that it is a square.

Prove the opposite sides of a Lambert quadrilateral are
parallel.

Prove in hyperbolic geometry: If two Saccheri quadrilaterals
have congruent bases and congruent summits, then they are
congruent.

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.

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

6. (a) Prove by contrapositive: If the product of two natural
numbers is greater than 100, then at least one of the numbers is
greater than 10. (b) Prove or disprove: If the product of two
rational numbers is greater than 100, then at least one of the
numbers is greater than 10.

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.)

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