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1. If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a parallelogram.

1. If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a parallelogram.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.3: Proving Triangles Similar
Problem 4E: Classify as true or false: a If the midpoints of two sides of a triangle are joined, the triangle...
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il VOLTE 8:09 p.m. 27% Janhavi K School < 7minuteseigolauncher.com HOTS 1. If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a parallelogram. 2. L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD, prove that DL, DK, BM and BN enclose a rhombus. 3. PQRS is a parallelogram. PS is produced to meet M so that SM = SR and MR is produced to meet PQ produced at N. Prove that QN= QR. 4. In a AABC, DE is parallel to BC and D is the mid- point of side AB. Find the perimeter of AABC when AE = 4.5 cm, DE = 5 cm and DB = 3.5 cm. 5. If an angle of a parallelogram is 4/5 of it adjacent angle, then find the measures of all the angles of the parallelogram. 6. ABCD is a trapezium in which AB is parallel to CD. If LA = 36° and LB = 81°, then find LC and LD. 7. In a AABC, DE is parallel to BC and D is the mid- point of side AB. Find AE and BC if DE = 6 cm and EC = 5 cm. 8. In a parallelogram ABCD find the measure of all the angles if one angle measures 68°. 9. The lengths of diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus. 10. In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice the smallest angle. in f •..
Transcribed Image Text:il VOLTE 8:09 p.m. 27% Janhavi K School < 7minuteseigolauncher.com HOTS 1. If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a parallelogram. 2. L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD, prove that DL, DK, BM and BN enclose a rhombus. 3. PQRS is a parallelogram. PS is produced to meet M so that SM = SR and MR is produced to meet PQ produced at N. Prove that QN= QR. 4. In a AABC, DE is parallel to BC and D is the mid- point of side AB. Find the perimeter of AABC when AE = 4.5 cm, DE = 5 cm and DB = 3.5 cm. 5. If an angle of a parallelogram is 4/5 of it adjacent angle, then find the measures of all the angles of the parallelogram. 6. ABCD is a trapezium in which AB is parallel to CD. If LA = 36° and LB = 81°, then find LC and LD. 7. In a AABC, DE is parallel to BC and D is the mid- point of side AB. Find AE and BC if DE = 6 cm and EC = 5 cm. 8. In a parallelogram ABCD find the measure of all the angles if one angle measures 68°. 9. The lengths of diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of the rhombus. 10. In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice the smallest angle. in f •..
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