Select one of the triangle theorems and write a proof for it.
2 answers:
Answer:
Look at the attached picture
Step-by-step explanation:
Yes, they are congruent by the SAS Theorem
From the figure, we see that there are two congruent pairs of corresponding sides, AC¯¯¯¯¯¯¯¯≅DF¯¯¯¯¯¯¯¯,BC¯¯¯¯¯¯¯¯≅EF¯¯¯¯¯¯¯¯, and one congruent pair of corresponding angles, ∠C≅∠F. The Side-Angle-Side Theorem (SAS) states that if two sides and the angle between those two sides of a triangle are equal to two sides and the angle between those sides of another triangle, then these two triangles are congruent.
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Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
• 1 + cot²x = csc²x
Consider the left side
x -
x
Factorise as a difference of squares
= (csc²x - cot²x)(csc²x + cot²x)
= (1 + cot²x - cot²x)(csc²x + cot²x)
= csc²x + cot²x
= csc²x + csc²x - 1
= 2csc²x - 1 = right side ⇒ verified