True/False
There are only four valid methods for proving triangles congruent in general, although in special cases other methods may be found.
True
(SAS, SSS, ASA, AAS)
If two lines are __________________________, then they create adjacent angles which are equal.
Perpendicular
Def. 10
In triangle CAB, m<A > m<C. If AB= 25 and BC= 3y + (7 - 2y).
What proposition will help us solve this problem?
Proposition 19 (I'll accept 18 too).
They're basically the same thing and sometimes even I can't remember which is which.
What are the 4 ways we can prove triangles congruent?
SAS, SSS, ASA, AAS
If the hilly billy then, the icy spicy.
If the hilly is not billy, what can we conclude? What is this called?
We can conclude the icy is not spicy
Modus Tollens
No obtuse triangles are also isosceles.
False
(All 3 angles need to add to 2 right angles, there can be 1 obtuse angle and 2 equal acute angles)
Any two lines which meet make _________________________ angles equal.
Vertical
Proposition 15
In triangle CAB, m<A > m<C. If AB= 25 and BC= 3y + (7 - 2y).
Write the inequality that will help us solve this problem.
Side BC > side AB
Proposition 10: What construction is almost exactly the same as the perpendicular bisector?
Equilateral triangle
What does Q.E.D mean in english?
that which was to have been demonstrated.
In any triangle, the difference in the lengths of two sides is always greater of the third.
False
(Triangle Inequality Theorem: In any triangle, the SUM in the lengths of two sides is always greater of the third)
. If the two sides of two adjacent angles which are not shared fall in a straight line, the angles are called a ____________________ _____________.
Linear pair
In triangle CAT, CA=12, AT= x+5 and CT= 2x-7.
What proposition will help us solve this problem?
Proposition 20
What do propositions 18 and 19 say?
The greater side/angle subtends (is opposite of) the greater angle/side.
What does Q.E.F mean in english?
that which was to have been done.
Given ANY three line segments, with a straight edge and a compass a triangle can be constructed with sides equal in length to the given three segments.
False
(The 3 line segments need to follow the triangle inequality theorem)
Any two angles, adjacent or otherwise, that add to equal two right angles are called _____________________.
Supplementary
In triangle CAT, CA=12, AT= x+5 and CT= 2x-7.
What is the name of the theorem proven in proposition 20?
Triangle Inequality Theorem
What does proposition 13 prove?
Angles that sit on top of a straight line are 2 right angles, or add up to 2 right angles.
What does Q.E.D mean in latin?
Quod Erat Demonstrandum
The converse of a statement may in some cases only be able to be proved indirectly.
True
(Propositions 7 and 26)
Any two angles, adjacent or otherwise, that add to equal one right angle are called _____________________.
Complimentary
In triangle CAT, CA=12, AT= x+5 and CT= 2x-7.
How many different inequalities should be written to solve this problem?
3 inequalities
CA + AT > CT
AT + CT > CA
CT + CA > AT
Why is proposition 15 relevant?
Proves that vertical angles are equal
What does Q.E.F mean in latin?
Quod Erat Faciendum