Answers:
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Explanation:
The diagram is below.
Draw two triangles that are identical copies of each other. This is exactly what the term "congruent" means. Congruent items are identical items.
The order is very important when it comes to figuring out congruent triangles. Triangle ABC has A first, B next, C last. For triangle DEF, we have D first, E next, F last.
This means we have this pairing:
- A pairs with D
- B pairs with E
- C pairs with F
Because the triangles are congruent, we know that:
- angle A = angle D
- angle B = angle E
- angle C = angle F
So if we could find out angle B, then we automatically will find out angle E as well.
Use the idea that for any triangle, the angles always add to 180
A+B+C = 180
34+B+124 = 180
B+158 = 180
B = 180-158
B = 22
Angle B is 22 degrees, and so is angle E.
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Everything in the previous section handled how to find angle E.
In this section, we'll find how long side DE is.
Since the angles pair up in the way mentioned earlier, we can further extend that idea to have these three pairs
- side AB pairs with side DE
- side BC pairs with side EF
- side AC pairs with side DF
The pairs are formed directly based on how the angles pair up. For instance, AB and DE are both the first two letters of ABC and DEF respectively. In the diagram, AB and DE are both the left slanted side. However, the diagram can sometimes be misleading because it's perfectly possible to rotate triangle DEF to not have it line up with ABC. I drew the diagram to help make the pairings as clear as possible.
Anyways, we have AB pair up with DE. Both of those pieces must be congruent if we want the overall triangles to be identical. We're told that AB = 24, which means DE = 24.
