Help with circled geometry proofs

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LiHJ
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Homework Statement



Dear Mentors,

Please guide me in solving the circled questions on the 2 attachments.

Homework Equations




Thank you

The Attempt at a Solution


 
Attachments
  • Geometry problem 16 with a diagram of parallelogram ABCD, diagonal AC, points H, G, E, F, and lines DE and DF; part (a) and part (b) are circled.
    geometry 1.jpg
    43.5 KB · Views: 437
  • Geometry problem diagram: semicircle with centre O and diameter AB, point P on the arc, PQ perpendicular to AB, inscribed circle centre C touching PQ at D, AB at E and the semicircle at F; part (d) AE = AP circled.
    geometry2.jpg
    22.1 KB · Views: 432
Why only Mentors?

There are other too to help you out. :)

But first you need to show your attempts. That will help us to know where you are stuck and we would help you to proceed. :)
 
For Geometry Ques 16b)

From my understanding, in order for me to prove 2 lines parallel, I need to have corresponding angles, alternating angles or supplementary angles. The following attachment is my working. The angle with the same colour marking is equal.

But I am stuck with to prove the angle on the line EF to be related with my other marked angles.

There is another attachment of my working for the other question.

Thank you.

I see everybody as my Mentor as they guide me in different ways.
 
Attachments
  • Hand-drawn geometry sketch of a parallelogram ABCD with points E, F, G and H on its sides and interior, with arrow marks on parallel segments and coloured angle markings.
    geometry 1 working.jpg
    31.1 KB · Views: 451
  • Handwritten geometry working on lined notebook paper: a labelled diagram with points A, B, C, D, E, F and a right-angle marker, followed by step-by-step angle proofs using alternate and supplementary angles, and a similar-triangles proof concluding AD x AF = AG x AB.
    geometry 2 working.jpg
    34 KB · Views: 453