Prove that Two Vectors are Colinear

﻿Hi, I'm Mr Bond and in this lesson, we're going to learn about the conditions of congruent triangles. In this lesson, we're thinking about conditions of congruent triangles. Congruent means the same. So, two triangles are congruent if they satisfy one of these criteria. If two sides and the included angle are the same in each triangle, then we can say that they're congruent. So that might look like this. The side, the included angle and the other side being the same in both triangles. We call this side angle side and we often abbreviate it, SAS. Here's another condition. We can also say triangles are congruent if two angles and the included side are the same. That might look like this. The angle, the included side and another angle being the same. We call this angle side angle and we often abbreviate it, ASA. Here's another condition. We can also say that they're congruent if all three sides are the same length. So that would obviously look like this. One side, another side and the third side being the same. We call this side, side, side and we often abbreviate it, SSS. Here's the final condition upon which two triangles can be congruent. If it's a right-angled triangle where the hypotenuse and one other side are the same, then we can also say that they're congruent. So that's where it's right angled, the hypotenuse and one side are the same. We call this right angle hypotenuse side and we often abbreviate it, RHS. Here's an example. Are the two triangles congruent and we need to state any conditions used. Well, have a look at the sides and the angles that are given. The two sides that are given in each triangle are the same and the angle's the same, but we need to make sure it's the included angle and it is for both triangles, so that means, yes, the triangles are congruent and the condition that we used was side angle side. Here's a question for you to try. We're told that each pair of triangles is congruent, you just need to state the condition of congruency used. Pause the video to complete the task and resume when you're finished. Here are the answers. Let's look at each one in turn. For part A, we know that two sides are the same and the included angle is the same, so that's side angle side. The second pair of triangles, we know that two angles and the included side are the same so that's angle side angle, and then for part C, we have two right angled triangles where the hypotenuse and one of the shorter sides is the same, so this is RHS, right angled hypotenuse side. Here's something for you to think about. Is the statement always, sometimes or never true? If we know two sides and an angle are the same in two triangles, we can decide if they're congruent using side angle side. Pause the video to have a think and resume the video when you've finished. Well, if we know two sides and the angle is the included angle, then we can use side angle side. But if it's not the included angle, then we can necessarily use side angle side, so this is only sometimes true. Here's another question for you to try. Pause the video to complete the task and resume the video when you've finished. Here's the answer. Lots of people get confused by this. It's particularly because side, side, side is a condition for congruent triangles, so people imagine that angle, angle, angle is also a condition, but it's not. Think about this. We could have a very large triangle with the same three angles, as a very small triangle. These two triangles will be similar, but not congruent. Here's another question for you to try. Pause the video to complete the task and resume the video when you've finished. Here are the answers. In this case, it's Amir that's correct. It's not necessarily the case that they're not congruent, but we can't be absolutely sure because the angle given isn't the included angle. Here's another example. Again, we want to know, are the two triangles congruent? And we need to state any conditions used. Well lets look at the information that we're given. We know two angles in each triangle and one side. So can we use angle side angle? Well we certainly can't immediately use angle side angle because the side that's given isn't the included side between the angles and the angles aren't the same in both triangles, or at least not the given ones. Because we know two angles in each triangle, we can use this and the fact that angles in a triangle sum to 180 to find the missing angle in each triangle. So for the triangle on the left, the missing angle is 59 degrees. And in the triangle on the right, the missing angle is 82 degrees. So let's take another look. Now can we say that the two triangles are congruent? Well, now that we can see that the 59 degrees and 82 degrees is the same in both triangles, and also, the five centimetre side is the included side between these angles for both triangles, yes, the triangles are congruent. And which condition have we used? Angle side angle. Here's the final question for this lesson. Pause the video to complete your task and resume the video when you've finished. Here's the answer. We can use the fact that we know the perimeter of both triangles to find the length of the missing side and then when we compare all three sides in both triangles, we see that they're the same, so they're congruent by side, side, side. That's all for this lesson, thanks for watching.

Conditions of Congruent Triangles

In this lesson, we will learn about the conditions under which we can say that two triangles are congruent.

Lesson overview:Conditions of congruent triangles

Higher Vectors 2 and Congruent Triangles: