True/False
If a statement is true, then its converse must be true as well.
False!
If its raining, its wet outside.
But, just because its wet outside doesn't mean it rained. A sprinkler could have come on.
___________ added to equals gives equals.
"Equals"
C.N.2
Give the converse of the following:
If Melissa is late to work, then she will get fired.
If Melissa has been fired, she was late for work.
What is the relevance of I.1?
It shows us that we can physically construct an equilateral triangle with a compass and a straight edge.
Is the following a common notion or a postulate? Which number is it?
To describe a circle with any centre and distance.
Postulate 3
All isosceles triangles have at least one pair of equal angles.
True!
In book 1 proposition 5 we proved this.
__________________ is the abbreviation of the latin term meaning "being what is required to prove" (roughly translated).
Give the converse of the following:
If the teacher is late to class, then he will get a raise.
If the teacher gets a raise, then he was late to class.
What is the relevance of I.3?
It shows us that given 2 unequal straight lines, we can cut a piece of the larger one equal to the smaller.
Which postulate is the following?
That, if a straight line falling on 2 straight lines make the interior angles on the same side less than 2 right angles, the 2 straight lines, if produced indefinitely, meet on that side on which are the angles les than the 2 right angles.
Postulate 5
If 2 triangles coincide, then only one pair of corresponding sides must be equal.
False!
All of the corresponding sides and angles are Equal.
If 2 triangles have 2 pairs of corresponding sides equal and the ____________________ equal, then the triangles are equal. [phrase]
angles in between
This is basically SAS congruence written out in words!
Give the converse of the following:
If the walzit is plobar, then the walzit is also exrut.
If the walzit is exrut, then it is also plobar.
What is the relevance of I.4?
SAS congruence is proven.
Which Common Notion deals with subtraction?
C.N.3
All angles must be either less than or equal to a right angle.
False!
Obtuse angles are bigger than right angles (:
A triangle is a ______________ figure bounded by _____________ straight lines.
1. Rectilinear
2. Three
State the conclusion that follows from the given premises:
P.1- If the walzit is plobar, then the walzit is also exrut.
P.2- The walzit is not exrut.
The walzit is not plobar.
What is the relevance of I.5?
Shows that the angles at the base of an isosceles triangle are equal, and if the 2 equal sides be extended, the angles under the base are also equal.
Which common notion is the following?"
Things which coincide with one another are equal to one another.
C.N.4
If 2 rectilinear angles are equal, then they can be made to coincide.
True!
Just slap one on top of the other, and now their coinciding.
The _____________ is the part of the proposition which says in general terms what is to be done or proved.
Enunciation
The part of the proof written in italics
What type of argument gives the following conclusion:
P.1- If the walzit is plobar, then the walzit is also exrut.
P.2- The walzit is not exrut.
Conclusion- The walzit is not plobar.
Modus Tollens!
The only argument type we will ever discuss; please do not miss this question.
What is the relevance of I.8?
SSS congruence is proven here!
Given: Isosceles triangle ABC where AB=AC. D is the midpoint of BC and AD is joined.
To prove: Angle ADB is a right angle.
Which of the 2 congruence theorems will prove this?
SAS