Cuánto es 7b + 2=23??
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Vertical angles are angles which are <u>opposite</u> to each other and have <u>equal</u> measures. With respect to the given proof, <em>Angie</em> completed the proof <em>incorrectly</em>.
<em>Two</em> angles are said to be <u>vertical</u> when they are <em>opposite</em> to one another and have <em>equal</em> measures. However, two angles are <u>supplementary</u> if they <u>add</u> <u>up</u> to 180°.
So, comparing Angie's and Becky's proofs, it can be deduced that from Angies proof:
1. Segment GH intersects segment AB at K (1. Given)
2. m∠AKG + m∠GKB = 180° (2. Definition of Supplementary Angles)
m∠GKB + m∠HKB = 180° (2. Definition of Supplementary Angles)
3. m∠AKG + m∠ GKB = m∠GKB + m∠HKB (3. Substitution Property)
4. m∠AKG = m∠HKB (4. Subtraction Property)
Note:
- Step 2 should be Angle Addition Postulate, since:
m∠AKG + m∠GKB = 180°
m∠GKB + m∠HKB = 180°
So that;
m∠AKG + m∠GKB = m∠GKB + m∠HKB
<u>Subtract</u> m∠GKB from both sides to have;
m∠AKG = m∠HKB (which is the proof for step 4)
Therefore, <u>Angie</u> completed the poof <em>incorrectly</em> because of the properties of steps 2 and 4.
A diagram is herewith attached for more clarifications.
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The reflection of BC over I is shown below.
<h3>What is reflection?</h3>- A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is known as the reflection's axis (in dimension 2) or plane (in dimension 3).
- A figure's mirror image in the axis or plane of reflection is its image by reflection.
See the attached figure for a better explanation:
1. By the unique line postulate, you can draw only one line segment: BC
- Since only one line can be drawn between two distinct points.
2. Using the definition of reflection, reflect BC over l.
- To find the line segment which reflects BC over l, we will use the definition of reflection.
3. By the definition of reflection, C is the image of itself and A is the image of B.
- Definition of reflection says the figure about a line is transformed to form the mirror image.
- Now, the CD is the perpendicular bisector of AB so A and B are equidistant from D forming a mirror image of each other.
4. Since reflections preserve length, AC = BC
- In Reflection the figure is transformed to form a mirror image.
- Hence the length will be preserved in case of reflection.
Therefore, the reflection of BC over I is shown.
Know more about reflection here:
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The question you are looking for is here:
C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.
