Let's analyze and solve the problems in the image.

Problem 28:

It looks like you were asked to find the missing side in a right triangle, likely using the Pythagorean theorem.

1. First triangle:

   • Given sides: 8 and 9.
   • The formula used is: $a^2 + b^2 = c^2$.
   • So, $8^2 + 9^2 = c^2$ becomes: $64 + 81 = c^2$ $145 = c^2$
   • Taking the square root on both sides: $c = \sqrt{145}$

   So, the missing side $c$ is $\sqrt{145}$.

2. Second triangle:

   • Given sides: 14 and 9.
   • Using the Pythagorean theorem: $14^2 + 9^2 = c^2$ $196 + 81 = c^2$ $277 = c^2$
   • Taking the square root on both sides: $c = \sqrt{277}$

   So, the missing side $c$ is $\sqrt{277}$.

Problem 30:

This problem asks you to complete a conditional statement related to a quadrilateral being a square.

• Given Conditional: "If a figure is a quadrilateral, then it is a square."

• True or False: You answered false, and this is correct because not all quadrilaterals are squares.

• Counterexample: Any quadrilateral that is not a square can be used as a counterexample. For instance, a rectangle, rhombus, or trapezoid.

• Converse: "If a figure is a square, then it is a quadrilateral." This is true because every square is indeed a quadrilateral.

Do you need more details or have any questions about these problems?

Here are 5 related questions:

1. How do you determine if a triangle is a right triangle using side lengths?
2. What other methods, besides the Pythagorean theorem, can be used to find missing sides in triangles?
3. What are the properties of different types of quadrilaterals?
4. How can you identify the converse, inverse, and contrapositive of a conditional statement?
5. What are some common mistakes to avoid when using the Pythagorean theorem?

Tip: When solving problems involving the Pythagorean theorem, always double-check the squares of the side lengths and ensure you're solving for the correct side (either a leg or the hypotenuse).