In Euclidean geometry, two triangles are known to be congruent if two corresponding angles and the side they contain are congruent. Two angles and the side are congruent if they have the same measure. This is called ASA congruence. ASA stands for angle, side, angle.
In figure 1, angles A and A' are congruent, angles B and B' are congruent and line segment AB is congruent with line segment A'B'.
Click on the blue points and drag them to change the figure. When you change the figure, what stays the same and what changes. Some things to look at are the length of the lines, the size of the angles, and the orientation. |
Manipulative 1 - Angle-Side-Angle Congruence of Triangles Created with GeoGebra. |
Step | Diagram | Discussion |
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Click on the blue points and drag them to change the figures. | ||
1 | Let ΔABC be any triangle. Let A'B'C' be a triangle such that that the angle A'B'C' is congruent with angle ABC, and angle B'C'A' is congruent with angle BCA and side a is congruent with side a'. Note that point D is used only to rotate the triangle. | |
2 | !!!!!UNKNOWN REFERENCE APPLETGGBasacongruence02.ggb!!!!! | Construct point C'' on line segment AC such that AC'' = A'C'. |
3 | Angles BCC'' = BAC = B'A'C' (given). Segments BC = B'C'. So, triangle BCC'' = B'A'C'. | |
4 |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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