MT1100 Problem Sheet 1 Due: Thursday 8th October at 10:00. Please write your name clearly at the top of each page. Scan your work as a single-file PDF. Do not use too high a resolution to ensure the file size remains below 20 MB (the upper limit is 50MB). Then upload your PDF file onto Moodle, as per the instructions available from the General Information box on Moodle. You are encouraged to leave your handwritten comments to the marker on the first or last page of your homework submission. Please submit by uploading a pdf containing your solutions to Moodle. This sheet asks you to write down some geometric proofs, using congruence of triangles and some of the definitions I gave this week. 1. A line L passes through the point A of a triangle ABC, and passes through a point D on the side BC: A a b e d c O B f D C L (i) Suppose L is an angle bisector. Which angles in the diagram above are equal? (Very briefly justify your answer.) (ii) Suppose L is an altitude. Which angles in the diagram above are equal? (Very briefly justify your answer.)
(iii) Suppose L is an angle bisector and an altitude. Show that |AB| = |AC|. Hint: First show that two triangles are congruent, by applying one of the rules. 2. For a parallelogram ABCD, show that ZA = LC and ZB = LD.