Playing with Congruent Triangles

(Scroll down if you want to see some explanations for this applet; enjoy!)

In this applet, with given base segment AB, you will get to play around and create a pair of congruent triangles in four different ways: SSS (side-side-side): In this case, we will construct two congruent triangles by drawing a circle centered at A with radius of r and another circle centered at B with radius of r₂, placing points C and C' at the two intersections of these two circles, and then creating triangles ABC and ABC'. Here, you will get to control the values of r and r'. Triangles ABC and ABC' are congruent to each other as these two triangles share side AB, AC = AC' = r, and BC = BC' = r_2.-- making each of the three sides of triangle ABC congruent to the corresponding side of triangle ABC'. SAS (side-angle-side): In this case, we will construct the two congruent triangles by drawing a circle centered at A with a radius of r, drawing two rays that each starts from A and forms an angle of value

from segment AB, and then placing points C and C' at the two intersections between the circle and one of the two rays -- forming triangles ABC and ABC' Here, you will get to control the values of r and

. Triangles ABC and ABC' are congruent to each other as these two triangles share AB, AC = AC' = r, and m -- making each of the two adjacent sides of triangle ABC congruent to the corresponding side of triangle ABC' & making the angle between those two sides in triangle ABC congruent to the angle between the corresponding sides in triangle ABC'. AAS (angle-angle-side): In this case, we will construct the two congruent triangles by drawing a pair of rays that each starts from A and forms an angle of value

from segment AB, then drawing a second pair of rays that each starts from a point along one of the first pair of rays (that is, C/C') and each forms an angle of value

from segment AC/AC', and finally placing B at the intersection of the second pair of rays. Here, you will get to control not only the values of and , but also the length of segment AB (in case you end up making the triangle too small or too big while playing around the value of the two angles). In this case, two triangles ABC and ABC' are congruent to each other, as they share base side AB, m<BAC = m<BAC' =

, and m<ACB = m<AC'B =

-- not only resulting in the two triangles sharing a congruent side, but also making an angle in contact with that side within triangle ABC congruent to the corresponding angle in triangle ABC' & making the angle not in contact with that side within triangle ABC congruent to the corresponding angle in triangle ABC'. ASA (angle-side-angle): In this case, we will construct the two congruent triangles by drawing two rays that start from A and each forms an angle of value

from segment AB and then drawing another two rays that start from B and each forms an angle of value

from segment AB. Here, you will get to control not only the values of

and

, but also the length of segment AB(in case you end up making the triangle too small or too big while playing around the value of the two angles). Triangles ABC and ABC' are congruent to each other as these two triangles share AB, m<BAC = m<BAC' =

, and m<ABC = m<ABC' =

-- not only resulting in the two triangles sharing a congruent side, but also making each of the two angles in contact with that side within triangle ABC congruent to the corresponding angle in triangle ABC'.

Playing with Congruent Triangles

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