Simplify each expression by using the distributive property and combining like terms.
2 answers:
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Answer:
Given in figure ABCD:
∠ABD≅∠CBD
AB≅CB
To prove:
∠A≅∠C
Solution:
In the figure ABCD, we will first prove the Δ ABD and Δ CBD are congruent.
Thus the proof can be given as:
Statement Reason
1) Given
2) Given
3) Reflexive property of congruence (As the segment is congruent to itself)
4) S.A.S (Side Angle side)
5) Corresponding parts of congruent triangles are congruent.
Hence proved.
<em><u>The slope of HI is 1/2 </u></em>
<em><u> The slope of EF is 1/2</u></em>
<em><u>Solution:</u></em>
Given that,
Triangle DEF is congruent to right triangle GHI
Which means,
These pairs of angles are congruent
{D, G}, {E, H}, and {F, I}
In triangle DEF, E is a right angle
This means that the line segments are perpendicular.
We know that,
Product of slope of a line and slope of line perpendicular to that line is equal to -1
Given that,
Slope of DE = -2
Since the sides EF and HI are congruent,
Slopes of parallel lines are equal
Thus, Slope of HI is 1/2