Vocabulary
Name this type of angle.
Reflex
Vertical angles have _______________ measure.
congruent
A triangle is a polygon with three sides and _________ angles.
3
Using the Angle-Angle Theorem, how many corresponding angles do you need to show are congruent to prove triangle similarity?
2
Since all angles of similar triangles are congruent, what missing measurements can you find with similar triangle properties?
Side lengths
How many degrees is a full rotation?
360 degrees
Two angles measurements that sum to 90 degrees are this type of angle pair.
Complementary
How many exterior angles sum to 360 degrees?
3
(not all bc there are 6)
Similar polygons must have congruent angles and _______________ side lengths.
proportional
(same scale factor)
How can you determine which sides of the triangles are corresponding?
Possible answers:
Mapping one triangle on top of the other
Match congruent angles
Rotate the triangles to resemble the same shape
What 2 parts of an angle do adjacent angles share?
Middle ray and vertex
Name a pair of alternate interior angles in the diagram.
<AEG <DGJ
<BEG <FGE
<CFE <BEF
<GFE <AEF
The sum of the 3 interior angles is always this.
180 degrees
Prove these triangles are similar.
Possible answer:
<DAC = 180 - (90 + 55)
= 35
Angle-Angle Theorem
Find the missing side length. NO ROUNDING
8
What is the difference between supplementary pairs and linear pairs?
Linear pairs must be adjacent
Name two angle pairs that are also supplementary pairs.
Same-side interior
Same-side exterior
Linear pair
Identify the two remote angles to the shown exterior angle.
<ABC <ACB
Prove these triangles are similar.
Possible answer:
x = 22
<QEF = 22 + 39
= 61
Angle-Angle Theorem
Find the missing side length. NO ROUNDING
14 2/3
14.6 repeating
How is an exterior angle of a triangle formed?
Extending a side passed the vertex
Write the equation to solve for x using angle relationships using the diagram.
21x + 6 = 90
Write an equation using the angle relationships in the diagram to solve for x.
7x + 5 + 60 = 20x
7x + 65 = 20x
Prove these triangles are similar
Possible answer:
<AEB congruent <CED vertical
<BAE congruent <CDE alt. interior angles
<ABE congruent <ECD alt. interior angles
Angle-Angle Theorem
A 7.5 foot ladder leans against a building and touches the wall 10 feet off the ground. A 15 foot ladder leans against the same building and is the same angle with the ground. How high off the ground does the 15 ft ladder touch the wall?
20 feet