Construction of Two Congruent Angles
To construct two congruent angles, you can follow these steps using a straightedge and a compass:
Step 1: Draw a horizontal line of any suitable length and label it AB.
Step 2: Place the compass tip at point B in the given angle. Draw an arc with BC as the base and label the point of intersection with the line YZ as D.
Step 3: Using the same compass width, draw an arc with the compass tip at point Y, labeling the intersection point with line YZ as O.
Step 4: Place the compass tip at point D and measure the arc from D to the intersection point of the arc with segment AB.
Step 5: Using the same arc, place the compass tip at point O and mark a cut on the arc drawn in step 3, labeling this point as X.
Step 6: Draw a line connecting points X and Y.
By following these steps, we obtain ∠ABC ≅ ∠XYZ, satisfying the definition of congruent angles. This construction demonstrates how to create an angle congruent to a given angle.
Congruent Angles
Congruent angles are angles that have equal measure. Thus, all the angles in the geometry that have sam measure are called congruent angles.
In this article, we will understand the meaning of congruent angles, their properties, the congruent angles theorem, the vertical angles theorem, the corresponding angles theorem, and the alternate angles theorem.
Table of Content
- What are Congruent Angles?
- Congruent Angles Theorem
- Vertical Angles Theorem
- Corresponding Angles Theorem
- Alternate Angles Theorem
- Congruent Supplements Theorem
- Congruent Complements Theorem
- How to Find Congruent Angles
- Constructing Congruent Angles
- Construction of a Congruent Angle to the Given Angle
- Construction of Two Congruent Angles
- Congruent Angles Properties
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