WEBVTT
00:00:01.460 --> 00:00:13.900
Consider two right-angled triangles where the lengths of the two perpendicular sides in one triangle are equal to the lengths of the corresponding sides in the other.
00:00:14.730 --> 00:00:16.470
Are these triangles congruent?
00:00:18.370 --> 00:00:25.530
This problem has given us a lot of information to answer a simple question, are these triangles congruent?
00:00:26.670 --> 00:00:34.220
Let’s swap through the information sketching out the triangles to determine if these two triangles are congruent or not.
00:00:35.960 --> 00:00:41.780
The first thing we know is that both of these triangles are right-angled triangles.
00:00:43.270 --> 00:00:47.300
We can start by just adding two right angles.
00:00:48.480 --> 00:00:52.830
One of these can be triangle A and the other can be triangle B.
00:00:54.070 --> 00:01:04.030
Next, we find out the lengths of the two perpendicular sides are equal in both of these triangles.
00:01:05.600 --> 00:01:08.820
One side can measure three centimetres.
00:01:09.960 --> 00:01:16.770
The other segment that makes up the right angle in both of these triangles could measure four centimetres.
00:01:18.500 --> 00:01:21.050
Currently, we don’t have triangles though.
00:01:21.400 --> 00:01:25.500
We just have two right angles made with line segments.
00:01:26.630 --> 00:01:33.980
You can fill in triangle A with the yellow line and triangle B with the pink line.
00:01:35.510 --> 00:01:38.860
How should we determine if these triangles are congruent?
00:01:40.350 --> 00:01:45.620
Congruent figures are always the same shape and the same size.
00:01:47.160 --> 00:01:52.330
These two figures — triangle A and triangle B — are the same shape.
00:01:52.660 --> 00:01:54.850
They’re both right triangles.
00:01:56.550 --> 00:02:01.060
But how can we determine if they are the same size?
00:02:03.970 --> 00:02:08.550
Well, one thing we could do is measure our third side.
00:02:10.120 --> 00:02:18.220
If each of these triangles have three sides that measure the same lengths, they are exactly the same size.
00:02:19.480 --> 00:02:31.680
If we measure our third side, the third side of triangle A is five centimeters and the third side of triangle B is five centimeters.
00:02:32.930 --> 00:02:42.780
This means triangle A has side lengths three, four, five and triangle B has side lengths three, four, five.
00:02:44.400 --> 00:02:48.710
These two triangles are exactly the same size.
00:02:49.450 --> 00:02:53.800
Same shape, same size make congruent figures.
00:02:55.620 --> 00:03:09.350
By carefully drawing out two figures and measuring them with a ruler, we find the description of these triangles produce two congruent figures.