Question

name: elijah.m date: 12-9-25 period: 6th unit 3 lesson 13: using the pythagorean theorem and similarity worksheet 1 1. basic parts of a right triangle - there are __ legs and hypotenuse - the meet at the right angle - the is the longest side and is always across from the right angle (with a right triangle image labeled a, b, c where c is the right angle) 2. the largest side of a triangle is across (opposite) from the the of a right triangle is always across from the 3. there is a relationship between the 2 legs and the hypotenuse: often pythagorean theorem is illustrated as the square of the sides as follows: (with an image of squares on the sides of a right triangle labeled a, b, c) the pythagorean theorem is . and c is always used for the __.

Explanation:

Step1: Recall Right Triangle Basics

A right triangle has 2 legs (the sides forming the right angle) and 1 hypotenuse (the side opposite the right angle, longest side).

Step2: Analyze Each Blank in Q1

• "There are \_\_\_ legs and \_\_\_ hypotenuse": A right triangle has 2 legs and 1 hypotenuse.
• "The \_\_\_ meet at the right angle": The legs (the two sides with the right angle between them) meet at the right angle.
• "The \_\_\_ is the longest side...": The hypotenuse is the longest side, opposite the right angle.

Step3: Analyze Q2

• "The largest side of a triangle is across from the \_\_\_": In any triangle, the largest side is opposite the largest angle. In a right triangle, the largest angle is the right angle, so the hypotenuse (largest side of right triangle) is opposite the right angle.

Step4: Analyze Q3 (Pythagorean Theorem)

The Pythagorean Theorem states that for a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). \(c\) is always the hypotenuse.

Answer:

Question 1:

• There are \(\boldsymbol{2}\) legs and \(\boldsymbol{1}\) hypotenuse.
• The \(\boldsymbol{\text{legs}}\) meet at the right angle.
• The \(\boldsymbol{\text{hypotenuse}}\) is the longest side and is always across from the right angle.

Question 2:

• The largest side of a triangle is across (opposite) from the \(\boldsymbol{\text{largest angle}}\).
• The \(\boldsymbol{\text{hypotenuse}}\) of a right triangle is always across from the \(\boldsymbol{\text{right angle}}\).

Question 3:

• The Pythagorean Theorem is \(\boldsymbol{a^{2}+b^{2}=c^{2}}\) (where \(a\), \(b\) are legs, \(c\) is hypotenuse). And \(c\) is always used for the \(\boldsymbol{\text{hypotenuse}}\).