Math Problem Statement
Do the following statement and its converse form a biconditional that is true?
If a triangle has a right angle, then it is right.
Solution
The given statement is:
"If a triangle has a right angle, then it is right."
Converse:
To check if the statement and its converse form a biconditional, we first need to find the converse of the statement.
The converse is:
"If a triangle is right, then it has a right angle."
Biconditional:
A biconditional statement is true if both the original statement and its converse are true.
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Original statement:
"If a triangle has a right angle, then it is right."
This statement is true because a triangle with a right angle is, by definition, a right triangle. -
Converse:
"If a triangle is right, then it has a right angle."
This is also true, since a right triangle is defined as a triangle with exactly one right angle.
Since both the statement and its converse are true, we can combine them into a biconditional:
"A triangle has a right angle if and only if it is right."
This biconditional is true.
Would you like more details, or have any questions?
Here are 5 related questions to expand on this:
- What is a biconditional statement, and how is it formed?
- Can you form a biconditional statement using other properties of triangles (e.g., equilateral triangles)?
- What is the difference between a converse and an inverse of a statement?
- How can a conditional statement be false, and what are examples of this?
- In what cases does the converse of a statement not hold?
Tip: Always check both the original statement and its converse when forming biconditional statements. Both must be true for the biconditional to hold.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Properties
Formulas
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Theorems
Properties of Right Triangles
Suitable Grade Level
High School