abcd is a rectangle in which diagonal ac bisects angle a and c?
441377
Given: ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. To Prove: (i) ABCD is a square. (ii) diagonal BD bisects ∠B as well as ∠D. and transversal AC intersects them.
204077
DEFINITION: A rectangle is a parallelogram with four right angles. THEOREM: If a parallelogram is a rectangle, it has congruent diagonals. THEOREM Converse: If a parallelogram has congruent diagonals, it is a rectangle. ... THEOREM: If a parallelogram is a rhombus, each diagonal bisects a pair of opposite angles.
787404
Problem 2: A rectangle is sometimes a square. The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.
1257248
The rectangle has the following properties: All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other). All angles are right angles by definition. The diagonals are congruent.
75163
Definition. A quadrilateral ABCD is a parallelogram if AB is parallel to CD and BC is parallel to DA. Assertion 1. If ABCD is a parallelogram, then the diagonals of ABCD bisect each other.
1090297
Theorem 16.5: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
1382272
ABCD is a trapezium in which AB||DC and its diagonals intersect each other at the point O. Show that `(A O)/(B O)=(C O)/(D O)` .
1388512
ABCD is a rectangle and O is the midpoint of AD ,P and Q are points on AB and CD ,respectively. such that AP=1/4AB and DQ=1/4DC. The ratio of area of the rectangle ABCD to that of the triangle OPQ is.
234647
ABCD is a cyclic quadrilateral in which AB and CD when produced meet at E and EA=ED. Prove that AD is parallel to BC and EB=EC.
1323331
In a rectangle, all the angles are equal and equal to 90 degrees. The diagonals of a rectangle are equal which is not equal in case of a parallelogram. In a parallelogram, diagonals are just bisectors, in a rhombus diagonal are perpendicular bisectors. The diagonals of a rectangle are congruent.
188533
If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
417947
ABCD is a quadrilateral P, Q, R, S are the points of trisection of the sides AB, CB, CD and AD respectively. Prove that PQRS is a parallelogram. ABCD is a quadrilateral in which P, Q, R, S are the points of trisection of the sides AB, CB, CD and AD respectively. ... Hence, PQRS is a parallelogram.
45277
The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB. Since ABCD is a rectangle, it is also a parallelogram. Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.
1094905
ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. Prove that .
212730
ABCD is a square of side 4cm. if E is a point in the interior of the square such that triangle CED is equilateral, then area of traiangle ACE.
708165
Correct answer: Explanation: A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem: where a and b are the sides of the rectangle and c is the length of the diagonal.
751475
ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal BD = 16 cm, then find the length of other diagonal AC. Side of Rhombus are equal.