1. CONGRUENT AND SIMILAR FIGURES
Unit 23
CONGRUENT AND SIMILAR FIGURES

2. CONGRUENT FIGURES
Congruent figures have exactly the same size and shape. The symbol  means congruent
Corresponding parts of congruent triangles are equal
The sides that lie opposite equal angles are corresponding sides
The angles that lie opposite equal sides are corresponding angles

3. CONGRUENT FIGURES A B C D
5"
4.75"
BCA and CAD are corresponding angles because they are both opposite 5" long sides
BAC and ACD are corresponding angles because they are both opposite 4.75" long sides

4. SIMILAR FIGURES
Similar figures mean figures that are alike in shape but different in size
Similar polygons have the same number of sides, equal corresponding angles, and proportional corresponding sides
The symbol ~ means similar

5. SIMILAR FIGURE EXAMPLE
Given that the two polygons shown below are similar and A = A', B = B', C = C', and D = D’, then A B C D A' B' C' D'
15.75"
16"
3.25"
3"
6"
The corresponding sides are proportional as follows:

6. SIMILAR FIGURE EXAMPLE (Cont)
Given that the two polygons shown below are similar and A = A', B = B', C = C', and D = D’,
Determine the lengths of sides (a) A'B', (b) B'C', and (c) C'D' A B C D A' B' C' D'
15.75"
16"
3.25"
3"
6"

7. SIMILAR TRIANGLES
If two angles of a triangle are equal to two angles of another triangle, the triangles are similar
If the corresponding sides of two triangles are proportional, the triangles are similar
If two sides of a triangle are proportional to two sides of another triangle and if the included angles are equal, the triangles are similar

8. SIMILAR TRIANGLES (Cont)
Within a triangle, if a line parallel to one side intersects the other two sides, the triangle formed and the given triangle are similar
If the altitude is drawn to the hypotenuse of a right triangle, the two triangles formed are similar to each other and to the given triangle

9. SIMILAR TRIANGLES EXAMPLE
Determine AD and DC in the right triangle shown below:
BD  AC so ABC ~ ABD ~ BDC B A D C
20 mm
15 mm
25 mm
DC = AC – AD = 25 mm – 16 mm = 9 mm Ans

10. PRACTICE PROBLEMS
Identify the pairs of corresponding angles in the figure below: B A E C D
3"
4"
5"

11. PRACTICE PROBLEMS (Cont)
The two polygons below are similar. A = A, B = B, C = C, D = D, E = E, F = F. Find each of the following:
Side BC
Side CD
Side DE
Side AF A B C D E F
10"
13.5"
12.5"
11.5"
9"
11" A B C D E F
8"

12. PRACTICE PROBLEMS (Cont)
CDE ~ ABE in the figure below. Given that AE = 70 ft, BE = 87.5 ft, EC = 25 ft, ED = 20 ft, and CD = 40 ft, find AB. A B E C D

13. PRACTICE PROBLEMS (Cont)
Determine length F in the figure below given that AB = 32 m and AC = 10 m.
50m F A C B

14. PROBLEM ANSWER KEY ABE and CED AEB and ECD BAE and EDC
a) inches
b) 10 inches
c) inches
d) inches
140 feet m