Question

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About topic QUADRILATERALS AND PARALLELOGRAM

ILLUSTRATE
• Provide one problem about in topic and solve it

EXPLAIN
• Explain how you solved the problem and describe the process you used to arrive at the solution.

1. Include any additional comments or reflections you would like to share about topic 1.​

Answer 1

Illustration

Problem:

Imagine a shape ABCD where AB is like a line on top and CD is a line at the bottom, and AD and BC are like the side edges. If the angle at the top corner A is 110 degrees, and the angle at the next corner B is 70 degrees, what are the angles at the other corners?

Solution:

Because of the way the lines are arranged, we know that angles at the top and bottom corners are the same, and angles at the side corners are also the same.

1. The angle at the top corner A is 110 degrees.

2. So, the angle at the other top corner C is also 110 degrees.

3. The angle at the next corner B is 70 degrees.

4. So, the angle at the other side corner D is also 70 degrees.

Explanation:

We figured this out by noticing that when you have lines running parallel, like AB and CD, or AD and BC, the angles on opposite corners are equal. So, we used that idea to find the angles at the other corners.

Additional Comments:

Understanding how angles work in shapes helps us solve problems. In this case, knowing that opposite angles are equal in this kind of shape (parallelogram) made it easier to find all the angles. Practice with different shapes helps us get better at using these rules.

Answer 2

Answer:

**Illustration:**

Problem: In parallelogram ABCD, the measure of angle A is 60 degrees and the measure of angle B is 120 degrees. Find the measure of angle C.

**Solution:**

To find the measure of angle C in parallelogram ABCD, we can use the property that opposite angles in a parallelogram are equal.

Since angle A is 60 degrees, angle C (opposite angle to angle A) is also 60 degrees.

Therefore, the measure of angle C is 60 degrees.

**Explanation:**

In a parallelogram, opposite angles are equal. This property arises from the fact that opposite sides of a parallelogram are parallel, and when a transversal intersects parallel lines, corresponding angles are equal.

Given that angle A is 60 degrees, we know that angle C must also be 60 degrees because they are opposite angles in parallelogram ABCD.

So, by applying the property of opposite angles in a parallelogram, we find that the measure of angle C is 60 degrees.

**Additional Comments:**

Understanding the properties of quadrilaterals and parallelograms is essential in geometry. Parallelograms have several unique properties, such as opposite sides being equal and opposite angles being equal. These properties make it easier to solve problems involving parallelograms by using geometric reasoning and relationships. Practicing problems like the one illustrated above helps reinforce these concepts and develop problem-solving skills in geometry.

A typical diagram illustrating the problem described above would look like this:

```

A _________ B

/ \

/ \

/ \

/ \

/ \

/___________________\

D C

```

In this diagram:

- Points A, B, C, and D represent the vertices of parallelogram ABCD.

- Angle A is 60 degrees, and angle B is 120 degrees.

- Since angle A and angle C are opposite angles in the parallelogram, angle C is also 60 degrees.