Download 2. Triangle inequality Theorem

Part 1
Unit 4-Review
Part 1- Triangle Theorems and Rules
Name of Theorem or
relationship
1. Side angle
relationship
In words/ Symbols
Diagrams/ Hints/ Techniques
 The longest side is across from
the largest angle.
 The medium length side is
across from the medium-sized
angle.
 The shortest side is across from
the smallest angle
2. Triangle
inequality Theorem
The sum of the lengths of the two
smaller sides of a triangle is greater
than the length of the largest side.
To find an inequality of possible sides,
add two given sides, subtract them.
3. Pythagorean
Theorem
a) c2 = a2 + b2
hypotenuse)
a) To find a missing
side
b) If c2 < a2 + b2 it is acute
If c2 > a2 + b2 it is obtuse
If c2 = a2 + b2 it is right
Draw arrows!
Add up the two smaller sides and
compare to the largest side. If the sum
is greater, it’s a triangle!
2,3,4
(2+3) > 4 ? yes!
C is longest side (
b) to Classify
triangles
If you see a right angle, it’s a right
triangle!  use P.T to solve for a
missing side.
WATCH OUT! If asked “does this make
a triangle” you must use Theorem # 2NOT PYTHAGOREAN.
ERROR ALERT: you must SQUARE
(power of 2) a, b and c, DIFFERENT
FROM Theorem #2 seen above.
4.Isosceles triangle
Theorem
The base angles of an isosceles triangle
are equal in measure.
The sides opposite the base angles in
an isosceles triangle (called legs) are
equal in length.
Angles opposite are congruent! If you
see expressions, make them equal to
each other!
5. Exterior angle
theorem
The measure of an exterior angle of a
triangle is equal to the sum of the
measures of the two remote interior
angles of the triangle.
IN + IN =OUT
Part 1
1) In triangle RQS, RQ= 10 inches, SQ =9 inches and RS= 8 inches, arrange the angles form smallest
to greatest.
2) The diagram at the right shows a right triangle with representations for two angles. What is the
value of x?
3) In triangle DOG, m∡D = 400 , m∡O= 600 ,, and m∡G = 800 ,.
State the longest side of the triangle __________________
State the shortest side of the triangle _________________
Classify the triangle based on its SIDES ___________________
4) State whether each of the following could be the sides of a triangle and why.
Part 1
a) {6,6,6}
b) {2,2,4}
c) {5,9,10}
d) {4,4,9}
5) Two sides of a triangle have lengths 2 and 7. Write an inequality for all possible integer lengths
of the third side.
6)
Given the following information find the degrees in each angle of the triangle.
<ABC = ________________
<BCA = ________________
<BAC = _______________
What is the longest side of the triangle? ___________________________
7) Determine whether the following sides form a right , acute or obtuse triangle. Justify your
answer with words.
a) 5, 11, 12
Part 1
b) 5, 12, 13
c) 7, 15, 18
8) Solve for x . Give
9)
your answer in the simplest radical form.
In the diagram below of DBCD , side DB is extended to point A.
(Note: The diagram above is not drawn to scale)
Which statement must be true?
(1) mÐC > mÐD
(2) mABC  mD
(3) mÐABC > mÐC
(4) mÐABC > mÐC + mÐD
10) In a triangle, the ratio of the angles is 1:3:5. Find the measure of all the angles and Classify the
triangle according to its angles.
Part 1
11)
Part 1
12). Consider the following diagram with 2 right triangles labeled, and the sides included in the diagram.
Solve for the whole length of side AC.