Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
In order to determine if two triangles are congruent, you can use SSS (side-side-side) or SAS (side-angle-side) properties. Triangles are congruent by SSS if all three sides of one triangle are congruent to a side of the other triangle. Triangles are congruent by SAS if two sides of one triangle are congruent to two sides of the other, and the angle between those sides is also congruent to the corresponding angle of the other triangle.
When the triangles make up a polygon, use information provided in the problem (such as where the midpoints are, etc.) to determine which side lengths are congruent.
A common problem for determining if you have two congruent triangles is to have triangles within a shape. So here we’ve got 1, 2, 3 triangles inside a rectangle.
Look at what we are given. We know that F is the midpoint, so the first thing that I’m going to do is I’m going to mark that EF and FG are congruent.
The second thing that you’re given is that you have an isosceles triangle here. Because if base angles are congruent that means that those two legs must also be congruent. So we have triangle EFI. EFI is talking about this triangle right here. Is it congruent to any other triangle in this box? And the answer is yes. We see that this triangle right here has three sides that are congruent to the three sides in this triangle. So what corresponds to angle E?
Angle E corresponds to angle G, how do I know that? E has one mark and two marks adjacent to it. G is the only angle over here that has one mark and two marks adjacent. So G is going to go first.
Next we have angle F. Angle F has one mark and three marks adjacent to it. And that’s the same in this triangle as well. So F is going to go second. Which means your remaining vertex is H, so triangle EFI is congruent to triangle GFH by, what short-cut do we use? We knew that 1, 2, 3 sides were congruent to 1, 2, 3 sides of the other triangle, so side-side-side.