Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =
1 answer:
Based on the triangle sum theorem, exterior angle theorem, the true statements are:
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
<h3>What is the Triangle Sum Theorem and the Exterior Angle Theorem?</h3>According to the triangle sum theorem, m∠2 + m∠3 + m∠5 = 180°.
Also, based on the exterior angle theorem, m∠2 + m∠3 = m∠6.
∠5 and ∠6 are a pair of linear angles, therefore: m∠5 + m∠6 = 180°.
In summary, the true statements about the diagram given are:
- m∠5 + m∠6 = 180°
- m∠2 + m∠3 = m∠6
- m∠2 + m∠3 + m∠5 = 180°
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What does this have to do with our problem? Well, we don't want to change the <em>value </em>of our fraction, we just want to change its <em>label</em>. So what we're going to do is multiply it by 1, but we're going to make sure to pick the right <em>label</em> for that 1.
7/12 x 1 = 7/12. This will be true no matter what. Let's see which of these options actually fit the bill:
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Nope, not quite. 14/28 is <em>not </em>equivalent to 7/12.
What about 21/36? 21 = 7 x 3, so let's give the form 1 = 3/3 a shot:
There we go! All we did there was <em>relabel </em>7/12 by multiplying by form of 1. Since we never changed its value, we can stop our search here and conclude that 21/36 is equivalent to 7/12.