Properties of Angle Bisectors and Symmetry
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1° Draw a straight angle $\widehat{sEl}$.
2° Draw its bisector $[Et)$.
3° Complete $\widehat{sEt} = \widehat{tEl} =$
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The line $(UK)$ is the axis of symmetry of the angle $\widehat{OUR}$.
1° What can you say of the angles $\widehat{KUR}$ and $\widehat{OUK}$.
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2° What does the semi-line [UK) represent to the angle $\widehat{OUR}$?
This question includes visual content: The image shows two geometric exercises. The first exercise features a horizontal line segment with endpoint 's' on the left, vertex 'E' in the center, and endpoint 'l' on the right, forming a straight angle. A perpendicular ray labeled 't' originates from 'E', created by compass construction arcs above point 'E'. The second exercise shows an angle $\widehat{OUR}$ with vertex 'U'. Ray $[UK)$ is drawn horizontally through the middle of the angle. One side of the angle, $UR$, is above $[UK)$ and the other, $UO$, is below it. Arcs indicate that $[UK)$ divides the angle.
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Let's work through these geometry problems involving angle bisectors and symmetry.
Geometry: Angle Bisectors and Symmetry
In the first part, we are asked to draw a straight angle s-E-l and then its bisector, E t.
Part 1: Bisecting a Straight Angle
A straight angle measures one hundred eighty degrees. When we draw the bisector, E t, we divide this angle into two equal parts.
So, the measures of the angles s-E-t and t-E-l are equal. Since one hundred eighty divided by two is ninety, each angle is ninety degrees.
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