diagonals

Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio. using the above theorem prove that a line through the point of intersection of the diagonals and parallel to the base of the trapezium divides the non parallel sides in the same ratio.

Question 33 Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Abcd is a trapezium in which ab parallel to dc and its diagonals intersect each other at point o

Expert-Verified Answer question 489 people found it helpful AkashMandal Given: ABCD is a trapezium where, AB ll CD Diagonals AC and BD intersect at point O. Construction: Draw a line EF passing through O and also parallel to AB. Now, AB ll CD, since by construction, EF ll AB ⇒ EF ll CD Consider the ΔADC, EO ll DC

Show that the diagonals of a square are equal and bisect each other at right angles

1. Opposite Sides are parallel 2. Opposite Sides are congruent 3. Opposite Angles are congruent 4. Consecutive Angles are supplementary 5. Diagonals bisect each other 6. Diagonals divide the parallelogram into two congruent triangles

Area of parallelogram formula using diagonals

Area given diagonals of a parallelogram and the angle between them area = ½ × e × f × sin (angle) The formula comes from trigonometry as well. Do you want to know where it comes from? Divide the parallelogram into two triangles, and assume that our e diagonal is the "base" for both new triangles. What's the height of that triangle?

The area of a rhombus with diagonals lengths as 7.5 cm and 12 cm is ______________.

02/14/2021 Health High School answered • expert verified find the area of a rhombus whose side is 7.5 cm and whose altitude is 4 cm if one of its diagonals is 8 cm long find the length of the Other diagonal See answer Advertisement podgorica Answer: Area square centimeter Diagonal centimeter Explanation:

The diagonals of a quadrilateral abcd intersect at o prove that

Question: 1. Which additional fact would prove that quadrilateral WXYZ is a parallelogram? 3. The diagonals of quadrilateral ABCD intersect at point K.

The diagonals of a quadrilateral abcd intersect each other

Solution Verified by Toppr Here, ABCD is a quadrilateral with diagonals AC and BD intersect at point E. ⇒ ECAE= EDBE [ Given ] ⇒ BEAE= EDEC ---- ( 1 ) In ABE and CDE, ⇒ BEAE= EDEC ] From ( 1 ) ] ⇒ ∠ABE=∠DEC [ Vertically opposites angles ] ∴ ABE∼ CDE [ By SAS similarity theorem ] ⇒ ∠EDC=∠EBA [ Corresponding angles are equal. ] ∴ ∠BDC=∠ABD

If the diagonals of a parallelogram are equal then show that it is a rectangle

Example: A parallelogram where all angles are right angles is a rectangle! Area of a Parallelogram Example: A parallelogram has a base of 6 m and is 3 m high, what is its Area? Area = 6 m × 3 m = 18 m2 Perimeter of a Parallelogram The Perimeter is the distance around the edges.

The diagonals of a quadrilateral abcd intersect each other at the point o such that show that abcd is a trapezium.

Solution GIVEN A quadrilateral ABCD whose diagonals AC and BD intersects at a point O such that AO OC = BO OD TO PROVE ABCD is a trapezium, i.e., AB ∣ ∣ DC. CONSTRUCTION Draw EO ∣ ∣ DC, meeting AD at E. PROOF In ΔACD,EO ∣ ∣ DC. ∴ AO OC = AE ED [ by Thale's theorme] But , AO OC = BO OD (give) ∴ BO OD = AE ED ⇒ DO OB = DE EA inΔAB.

Abcd is a trapezium in which ab parallel to dc and its diagonals

In a trapezium ABCD, AB is parallel to DC and the diagonals intersect at O. Show that OA: OC=OB: OD. If AB=2DC, show that O is the point of trisection of both the diagonals. Login Study Materials NCERT Solutions NCERT Solutions For Class 12 NCERT Solutions For Class 12 Physics NCERT Solutions For Class 12 Chemistry