If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Class 10 (Foundation)

### Unit 9: Lesson 2

Proofs using congruence

# Geometry proof problem: congruent segments

Sal proves that two pairs of segments are congruent using the ASA and AAS congruence criteria. Created by Sal Khan.

## Want to join the conversation?

• What is a chord?
• A chord is a line segment within a circle that touches 2 points on the circle.
• if you don't put a congruence symbol, then you're supposed to put an "m" in front of an angle statement ( m<A=m<C), right?
• yes, it stands for "the meausre of angle A = to the measure of angle C
• But how would you calculate the angle of a congruent triangle's angle when it isn't given on the other side, like adding/multiplying/deviding/subtracting from surrounding angles to find the angle of x, like in some of the Practices on the learning dashboard? I can't find a video for that |:(|)
• In the Congruent Triangles 2 problem set, you are still using the ideas covered in this set of videos (plus the "triangle angles sum to 180" and angle congruency rules). So when you are trying to figure out what x is try these common approaches:
1) see if it is equal to any of the angles you already have, maybe through vertical angles, for instance.
2) see if you can calculate it through the triangle-sum=180 rule - if you have the other two angles in the triangle, subtract them from 180 to get your angle
3) see if the other triangle in the diagram is congruent. If you have matching sides and angles enough to say the two triangles are congruent, then you can match them (carefully, so the correct angles/sides align) and find out what x is by grabbing it's congruent value.

As they get trickier, you will have to combine these approaches to get an answer.

Hope that helps!
• can you say ctcpc as the reason for #5
• Yes, because you proved that the triangles are congruent in the previous step, so therefore, everything thing is congruent in both triangles
• how are adjacent agnles congruent?
• Hold up. How would you know which step to do first when doing proofs? Do you just pick two lines/angles/sides, and then put them in the proof?

+proofs are hard+
• Start with the given, and then the order won't really matter. I'd recommend marking up the diagram first
• The other way to prove ED=EF is join AD .From this we can observer that AED and AFD are two congruent triangles because AD is the common side .angle DAE= angle DAF ( same vertex A).
and AE=AF (already proved ).Hence by SAS we can say the two triangles are congruent .Implies sides ED and EF are corresponding sides,hence Proved :)
• That assumes that AD bisects angle EAF. I think you can prove it but I'm not sure you can assume it even though it looks like it does. Anyone else have a thought about this?
• For proving ED=DF, wouldn't it have been much easier if you constructed a bisector in angle BAC and using ASA method?
• Could you please specify at what time in the video, so that I don't have to watch the full video to figure out where would be your question regard to.