1. [4 marks] Either redraw (it does not need to be perfect) or print the image below: D A E B C F (i) Shade in the quadrilateral EIABCE. (iii) Label angle dBAE as :15. (ii) Shade in the triangle ACFE. (iv) Label angle .L'AED as 3;. 2. [4 marks] Recall Ihales' -'l Theorems: 1. Vertical angles are equal 2. The angle sum of a triangle equals two right angles 3. The base angles of an isosceles triangle are equal. 4. An angle inscribed in a semicircle is a right angle. In gures a) and b) solve for 1' while only using Thales' four theorems. [11 your solution. briey state the steps that you took. (include which theorems you used). a) A bl \"\"530". 7' =43\" LCAO=30", x =aco O is the circle center 3. [2 marks] Using a ruler and a compass, draw an equilateral triangle with side lengths 3cm. 4. [2 marks] Using a ruler and compass, find the midpoint of the line segment AB below. Note: if you do not have a printer, you may draw your own line segment (of any size) on a piece of paper. A 5. [2 marks] Solve for a in the following figure. Note that O is the center of the circle. 7x+1 O 4x+16. [5 marks] Following the instructions in Lecture 7, find a square with the exact area of the rectangle below. Note: if you do not have a printer, you may draw your own rectangle (of any size) on a piece of paper. 7. [3 marks] In the following figure, AC = AD and AB = AE. AC = AD AB = AE (i) How do you know that ZABC is congruent to (equal to) LAED. (ii) How do you know that ZACD is congruent to (equal to) ZADC. (iii) How do you know that AABC is congruent to AAED. (iv) Show that BC = DE.NATS1920, Assignment 2 (38 marks) Due : Oct. 22 by 11:59pm 8. [3 marks] Solve for angle r in the following figures. Note that the lines AB and CD are parallel. b) A . B X C) A B 35 35 AB II CD AB II CD 9. [4 marks] Show that AABC is congruent to ACDE. Note that the quadrilateral below is a rectangle. BC = CD 10. [4 marks ] Solve for r. Note that the lines AB and CD are parallel. F 130 G F B ZAHG=130', ZCEG=135', x=ZHGE11. [3 marks ] Find the area of the triangle AABC and the parallelogram OBCED. 12. [2 mark] Consider the figure below. If you were to solve for x you would find x = -30, which is impossible! Something is geometrically wrong with this image. Briefly explain or show mathematically what the problem is. B 50 X+20 A C D