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MTH-4102-1
Supplemental Exercises
Geometry III
1. Identify the isometry that transforms figure A into image B.
2. Perform the following isometric transformations:
3. Find the image of the following polygons by applying the appropriate isometry:
4. Draw the image of the following polygons under the appropriate size
transformation:
5. Construct the following triangles with the aid of a ruler and a compass:
a) Triangle ABC, right angled in B, with angle C 28° and side BC measuring 3.7 cm.
b) An equilateral triangle with sides 4 cm.
c) A right isosceles triangle with congruent sides measuring 3 cm.
d) A triangle with 2 congruent 48° angles, with a 5 cm side between the two angles.
e) Triangle DEF, with angle D 45°, side DE 3.5 cm and side DF 4.9 cm.
6. Identify the following pairs of CONGRUENT triangles. Name the property which
allows you to make this affirmation:
7. Identify the following pairs of SIMILAR triangles. Name the property which
allows you to make this affirmation:
8. Identify the following pairs of SIMILAR triangles. Name the property which
allows you to make this affirmation:
E) Two triangles have sides respectively measuring 10 cm, 15 cm, 20 cm and 20 cm,
30 cm, 40 cm. Are these two triangles similar? Why or why not?
9. Determine whether the following pairs of triangles are congruent, similar or
neither. Justify your answer.
F) Two angles of a triangle measure respectively 39° and 65°. Two angles of another
triangle measure respectively 76° and 65°. Are these two triangles congruent? Why
or why not?
10. Given the following similar triangles where RS = 16 cm, RT = 15 cm, MT = 10 cm
and NT = 12 cm. Find the measure of sides MN and TS.
11. Find the measure of sides EF and OM.
12. Find the measures of sides KL and OL.
13. The ratio of similitude between the following pair of triangles is 6:1. Find the
measure of sides KM and ML.
14. The ratio of similitude between the following pair of triangles is 1:4. Find the
measure of sides ST and RT. (TRIANGLES ARE NOT DRAWN TO SCALE!)
15. Given the following similar triangles where NO = 4 cm, SR = 6 cm, ST = 5 cm
and RT = 4 cm. Find the measure of sides OM and MN.
16. Find the measures of sides DE and FE.
17. Find the measures of sides AB and EA.
18. Given the following similar triangles where DB = 6 cm, DE = 5 cm, EB = 6 cm
and AC = 6 cm. Find the measure of side CB.
19. Given the following similar triangles where RT = 13 cm, ST = 12 cm, and the
ratio of similitude between the two triangles is 2:5. Find the measure of sides MN
and RN.
20. Given the following similar triangles where AD = 3 cm, DF = 3.5 cm, AF = 2 cm
and BE = 4 cm. Find the measure of sides BC and CE.
21. Find the measures of sides QR and RP.
22. Calculate the measures of the missing sides in the following similar polygons:
a) k = 2/1
Find the measure of C'D'
b) Find the measures of B'F' and C'D'.
c) k = 1/4
Find the measure of A'B' and B'D'.
d) Find the measure of CD
e) Find the measure of the following sides:
f) Find the measures of the following sides:
23. Given the following diagram. Reproduce the plan to a scale of 1:1000
24. Given the following diagram. Reproduce the plan to a scale of 1:4
25. Given that the two sails are similar determine the measures of the 3 sides of the
sail DEF.
26. Similar triangles are used to indirectly measure large distances. For each of the
scenarios below, find the missing side:
a) The width of the lake AE:
b) The height of the tree: (why there’s a cowboy… I have no idea)
c) The width of the river:
d) Calculate the height of the mother, knowing that the height of the child is
0.80 m
e) What is the distance separating Emily from the house, knowing that Emily
is 105 cm tall and the house is 6.25 m tall.