show that the bisected of the angles of parallelogram enclose a rectangle
Answers
Answered by
2
Answer.
Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADC To prove: LKJI is a rectangle ∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary   [Since sum of adjacent angles of a parallelogram are supplementary] ΔABJ is a right triangle since its acute interior angles are complementary Similar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90° Then ∠JIL = 90° as ∠AID and ∠JIL are vertical opposite angles Since three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle. Thus LKJI is a rectangle.
Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADC To prove: LKJI is a rectangle ∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary   [Since sum of adjacent angles of a parallelogram are supplementary] ΔABJ is a right triangle since its acute interior angles are complementary Similar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90° Then ∠JIL = 90° as ∠AID and ∠JIL are vertical opposite angles Since three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle. Thus LKJI is a rectangle.
Attachments:
Answered by
1
answer ✨
__________
Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADC To prove: LKJI is a rectangle ∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary[Since sum of adjacent angles of a parallelogram are supplementary] ΔABJ is a right triangle since its acute interior angles are complementary Similar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90° Then ∠JIL = 90° as ∠AID and ∠JIL are vertical opposite angles Since three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle. Thus LKJI is a rectangle.
hope it will help you ✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨
__________
Given: ABCD is a parallelogram. AE bisects ∠BAD. BF bisects ∠ABC. CG bisects ∠BCD and DH bisects ∠ADC To prove: LKJI is a rectangle ∠BAD + ∠ABC = 180° because adjacent angles of a parallelogram are supplementary[Since sum of adjacent angles of a parallelogram are supplementary] ΔABJ is a right triangle since its acute interior angles are complementary Similar in ΔCDL we get ∠DLC = 90° and in ΔADI we get ∠AID = 90° Then ∠JIL = 90° as ∠AID and ∠JIL are vertical opposite angles Since three angles of quadrilateral LKJI are right angles, hence 4th angle is also a right angle. Thus LKJI is a rectangle.
hope it will help you ✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨✨
Attachments:
Similar questions