TRIANGLE CONGRUENCE
SSS, SAS, ASA, AAS, HL
You observe that every square you have seen is also a rectangle. You conclude that this is true for all squares. Is this inductive or deductive reasoning?
Inductive reasoning
"If Harry jogs home from school today, then he will go home by bicycle tomorrow." What is the conclusion?
He will go home by bicycle tomorrow.
What is the sum of the interior angles of any triangle?
180
True or False: If two parallel lines are cut by a transversal, then alternate interior angles are supplementary.
false
Why doesn't AAA prove congruence?
AAA only proves that triangles are similar not necessarily congruent
You notice a pattern in a sequence of shapes: a triangle, then a square, then a pentagon. You predict the next shape will be a hexagon. What type of reasoning is this?
inductive reasoning
"If Alexandra has symptoms of her pollen allergy, then it is springtime." Which statement is logically equivalent to this one?
if Alexandra does not have symptoms of her pollen allergy, then it is not springtime.
In an equilateral triangle, what is the measure of each interior angle?
60
Which two combinations of corresponding parts do not prove that two triangles are congruent?
SSA and AAA
The general rule is that all rectangles have four right angles. You are given a specific quadrilateral that is a rectangle. You conclude that this specific quadrilateral has four right angles. Is this inductive or deductive reasoning?
deductive reasoning
In the statement "If I eat a whole pizza, then I will be full." What is the hypothesis and what is the conclusion?
The hypothesis is "I eat a whole pizza" and the conclusion is "I will be full."
True or false: The Triangle Sum Theorem applies only to right triangles.
False
What is the specific requirement for the Hypotenuse-Leg theorem to be used?
HL is a special case that applies only to right triangles.
Vertical angles are congruent. Angles 1 and 2 are vertical angles. Therefore, angles 1 and 2 are congruent. What type of reasoning is used here
deductive reasoning
If a shape is a square, then it has four equal sides. What is the hypothesis and the conclusion?
A shape is a square, It has four equal sides
What is the name for angles that are located inside a triangle?
Interior angles
If you have two sides and the angle between them that are congruent in two triangles, which theorem can you use?
SAS
You see several angles that are all 90 degrees, and you conclude that all right angles must be 90 degrees. Is this an example of inductive or deductive reasoning?
Inductive reasoning. You are making a general conclusion based on multiple specific observations.
"Early to bed and early to rise, makes a man healthy, wealthy, and wise." Rewrite this as a conditional statement.
If a person goes to bed early and wakes up early, then they will be healthy, wealthy, and wise.
True or False: Every triangle, no matter the size, has interior angles that add up to exactly 180
true