Module 5 Lesson 2 Part 2 Writing Proofs

Module 5 Lesson 2 Part 2Writing Proofs Proving Triangles Congruent(Remember to print the Learning Guide notes that go with this lesson so you can use them as you follow along.)

This powerpoint is about module 5 lesson 2 part 2 writing proofs. Remember to print the Learning Guide notes for this lesson so that you can use them to follow along with parts of this powerpoint.1You have studied proofs in earlier modules.Remember that you always start with the given information.MARK that information on the diagrams. This is KEY! That is the only way you will know if it is SSS or SAS, etc.For each step in the proof, you must give a reason.

You studied proofs in earlier modules. Remember that the first step is always the given information. Before you even begin working on the proof, mark that given information in the diagrams. This is KEY in this modules because that is the only way you can determine how the triangles are congruent (if it is SSS or SAS or ASA, etc.). For each step in the proof, you must give a reason.2Possible reasonsGivenPropertiesReflexive (AB = AB) (very useful when triangles share a side)Symmetric Transitive

Definition of _________Definition of perpendicular linesDefinition of midpointDefinition of segment bisectorDefinition of angle bisectorDefinition of congruent segments

TheoremsVertical angles are congruent.All right angles are congruent.If 2 parallel lines are cut by a transversal, alternate interior angles are congruent.If 2 parallel lines are cut by a transversal, corresponding angles are congruent.SSS, SAS, ASA, AAS and HL

There are many possible reasons for each step in a proof. The reason for the first step is always given. Then you might use a property like those listed here. Or you might use a definition of a word and some examples are listed here. You might use a theorem and several of those that you have already learned are listed here. The tests we learned for congruent triangles (like SSS) are theorems too.31. Look at the given information and MARK it in the diagram. What you are given can lead to more steps in the proof (everything is given for a reason!)For example, if you are given an angle bisector, you will have a pair of congruent angles.You need to MARK them in the diagram and also state that the angles are equal in the proof.

How do I start a proof??

Many students struggle with proofs and do not know how to start. Always look at the given information and make sure you MARK it in the diagram. Then look at the given again and see what other information you know from that. What you are given will lead to more steps in the proof. For example, if you are given an angle bisector, you know that the angles on each side of the bisector are congruent. You will have to MARK them in the diagram and then STATE that they are equal in the proof.4

2. Look for shared sides.If the two triangles share a side, MARK THEM IN THE DIAGRAM and state it in the proof.

Statement: OM = OMReason: Reflexive Property

Once you have finished the given, then there are a couple more things you might see that can be useful. Be sure to look and see if the triangles share a side. If they do, MARK IT in the diagram and then that will be a statement in the proof. For example, look at this picture. The side OM is in both triangles so they share it. Put a mark on it (Or two marks) to show that it is congruent to itself. The statement in the proof will be OM = OM and the reason will be the reflexive property (since the segment is equal to itself).53. Look for vertical angles.If you see an X in the diagram anywhere, those are vertical angles. MARK THEM IN THE DIAGRAM and state it in the proof.

Statement: