WEBVTT
00:00:01.659 --> 00:00:07.229
Which congruence criteria can be used to prove that the two triangles in the given figure are congruent?
00:00:07.539 --> 00:00:12.399
Option (A) SSS, option (B) SAS, option (C) ASA.
00:00:12.399 --> 00:00:15.899
In this question, weโre asked for a congruence criteria.
00:00:15.899 --> 00:00:22.429
If we look at the options here, we can see that the S refers to side and the A represents angle.
00:00:22.489 --> 00:00:30.599
So, letโs look at our two triangles, ๐ด๐ต๐ถ on the left and triangle ๐ธ๐ท๐น on the right.
00:00:31.019 --> 00:00:36.059
Weโll make a note of any corresponding pairs of angles or sides which are congruent.
00:00:36.459 --> 00:00:43.829
In triangle ๐ด๐ต๐ถ, we can see that this angle ๐ด๐ต๐ถ is marked as 104 degrees.
00:00:44.069 --> 00:00:48.399
The same is true of angle ๐ธ๐ท๐น in triangle ๐ธ๐ท๐น.
00:00:48.659 --> 00:00:52.199
Therefore, we could say that these two angles are congruent.
00:00:52.819 --> 00:00:59.769
We can see that angle ๐ด๐ถ๐ต is 22.8 degrees and so is angle ๐ธ๐น๐ท.
00:01:00.079 --> 00:01:03.049
So, we have another pair of congruent angles.
00:01:03.529 --> 00:01:14.059
We can see that there are two sides which are marked as 7.1, side ๐ด๐ถ on triangle ๐ด๐ต๐ถ and side ๐ธ๐น on triangle ๐ธ๐ท๐น.
00:01:14.319 --> 00:01:16.619
Therefore, these sides are congruent.
00:01:17.039 --> 00:01:25.299
What weโve shown here is that we have angle-angle-side, so we could use the angle-angle-side rule to prove congruence.
00:01:25.539 --> 00:01:31.829
We could say that triangle ๐ด๐ต๐ถ and triangle ๐ธ๐ท๐น are congruent using the AAS rule.
00:01:32.089 --> 00:01:37.029
A quick reminder that the order of letters is important when describing congruence.
00:01:37.129 --> 00:01:44.439
For example, we know that angle ๐ถ in triangle ๐ด๐ต๐ถ is congruent with angle ๐น in triangle ๐ธ๐ท๐น.
00:01:44.599 --> 00:01:50.429
We know that angle ๐ต and angle ๐ท are congruent, and angle ๐ด and ๐ธ are congruent.
00:01:50.649 --> 00:01:54.259
So, when we look at the answer options, we see a problem.
00:01:54.399 --> 00:01:57.799
The AAS rule is not listed as an option.
00:01:57.989 --> 00:02:02.089
So, letโs see if we could prove congruence using another rule too.
00:02:02.369 --> 00:02:05.739
We donโt know any additional information about the length of the sides.
00:02:05.909 --> 00:02:07.809
So, letโs have a look at the angles.
00:02:08.349 --> 00:02:26.849
If we look at angle ๐ต๐ด๐ถ in the first triangle and angle ๐ท๐ธ๐น in the second triangle, we could actually work out the value of these angles by subtracting 104 and 22.8 from 180 degrees, as we know that there are 180 degrees in total in the triangle.
00:02:27.109 --> 00:02:31.389
So, both of these angles would be equal to each other; theyโre congruent.
00:02:31.659 --> 00:02:35.279
Weโve also just proved that these two triangles are congruent.
00:02:35.509 --> 00:02:39.409
Therefore, we know that these third angles must also be congruent.
00:02:39.809 --> 00:02:47.979
So therefore, if we take into account these last three pieces of information, we have two angles and the included side.
00:02:48.189 --> 00:02:50.889
Therefore, we have the ASA rule.
00:02:51.039 --> 00:02:59.419
So, weโve shown that these triangles are congruent using the ASA rule as well, which was the answer given in option (C).