- Answer: for this you will simply have to
**use**the**straightedge**to draw two parallel lines and then you draw a line that goes through them that is perpendicular. You then**use**the**compass**to measure the**angles**, they should be**congruent**and adjacent. I hope it helps, Regards.

## How can you use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle?

Answer Expert Verified

Answer: for this you will simply have to **use** the **straightedge** to draw two parallel lines and then you draw a line that goes through them that is perpendicular. You then **use** the **compass** to measure the **angles**, they should be **congruent and adjacent**.

## How do you construct a copy of an angle using a compass and straightedge?

- STEPS:
**Using**a**straightedge**, draw a reference line, if one is not provided.- Place a dot (starting point) on the reference line.
- Place the point of the
**compass**on the vertex of the given**angle**, ∠ABC (vertex at point B). - Stretch the
**compass**to any length that will stay “on” the**angle**.

## How do you construct with a compass and straightedge?

**The most-used straightedge and compass constructions include:**

- Constructing the perpendicular bisector from a segment.
- Finding the midpoint of a segment.
- Drawing a perpendicular line from a point to a line.
- Bisecting an angle.
- Mirroring a point in a line.
- Constructing a line through a point tangent to a circle.

## What does congruent mean?

**Congruent** means same shape and same size. So **congruent** has to **do** with comparing two figures, and equivalent means two expressions are equal.

## What are the steps in constructing congruent angles?

**Draw an arc that crosses both rays of the original angle.**

- Set the point of the compass at point B, the vertex of the original
**angle**, and draw an arc that crosses both Ray BA and Ray BC. You do not need to draw an entire circle. - For reference, mark the points where the arc crosses the rays as points X and Y.

## How do you construct a copy of an angle with a compass?

**Refer to the figure as you work through these steps:**

- Draw a working line, l, with point B on it.
- Open your
**compass**to any radius r, and**construct**arc (A, r) intersecting the two sides of**angle**A at points S and T. **Construct**arc (B, r) intersecting line l at some point V.**Construct**arc (S, ST).

## How do you construct a 45 degree angle with a compass?

**45 Degree Angle**

**Construct**a perpendicular line.- Place
**compass**on intersection point. - Adjust
**compass**width to reach start point. **Draw**an arc that intersects perpendicular line.- Place ruler on start point and where arc intersects perpendicular line.
**Draw 45 Degree**Line.

## Why is it important to use a compass and straightedge?

The **compass and straightedge** is more **important** in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a **compass and straightedge** cannot be seen at first glance and this situation become a problem for students.

## Why is doubling cubes and squaring circles impossible?

This is because a **cube** of side length 1 has a volume of 1^{3} = 1, and a **cube** of twice that volume (a volume of 2) has a side length of the **cube** root of 2. The impossibility of **doubling** the **cube** is therefore equivalent to the statement that ^{3}√2 is not a constructible number.

## What is the first step in constructing a congruent segment?

Two **segment** is said to be **congruent segment** if the measure of both **segments** are same and identical to each other. So, for drawing **congruent segments** firstly we have to measure the **segment**. Then draw a point. and lastly draw a ray.

## What is a congruent segment?

**Congruent** angles are angles that have the same measure. **Congruent segments** are **segments** that have the same length. Two points (**segments**, rays or lines) that divide a **segment** into three **congruent segments** trisect the **segment**. The two points at which the **segment** is divided are called the trisection points of the **segment**.

## When bisecting segments and angles which step is the same?

⇒So, to bifurcate something that is **segments and angles**, you need either a line or line **segment**. ⇒So, the two **steps** which are **same** is, **when bisecting segments and angles** is, Option A→Draw a ray with one endpoint. Option C→Draw a ray from the vertex to another point.