The least amount of information needed to establish congruence is; Angles M and M' are congruent, and angles N and N' are congruent.
<h3>What is the least amount of information needed to determine if the two triangles are similar?</h3>
If follows from concept of congruence that two triangles are congruent only if all three angle measures are congruent or all corresponding sides are in the same ratio.
Hence, when angles M, N and M', N' are established as congruent, it follows that the measures are equal respectively.
Ultimately, the measure of angles L and L' are equal and hence, all three angles are congruent in each triangle.
Therefore, the least amount of information needed is; Angles M and M' are congruent, and angles N and N' are congruent.
Read more on congruent triangles;
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ANSWER
(-1,2)
EXPLANATION
The given quadratic expression is:
The coefficient of the quadratic term is already 1.
So we add and subtract the square of half the coefficient of x.
We factor the first three terms to obtain
This is now in the form:
where (h,k) which is equal to (-1,2) is the vertex.
If Karen works 1 hour, she prepares 2 kg of dough.
If Karen works 2 hours, she prepares 2 kg + 2 kg of dough.
Maybe you can see where this is going.
If Karen works 3 hours, she prepares 2 kg + 2 kg + 2 kg of dough.
If Karen works h hours, she prepares 2 kg + 2 kg + ... + 2 kg of dough, where the number of instances of 2 kg is equal to h.
Early in your math career, you learned that repeated addition can be represented by multiplication. That is, when Karen works 3 hours, she prepares 3*(2 kg) of dough. It is not that big of a stretch to see that when Karen works h hours, she will prepare h*(2 kg) of dough.
Karen's output = h*(2 kg) . . . . . . an equation for finding the amount of dough
You are asked to solve this when h=5.
Karen's output = 5*(2 kg)
Karen's output = 10 kg
If she works 5 hours, Karen can prepare 10 kg of dough.
There are a few relations related to tangents and secants that you are expected to remember. These problems make use of those.
1. When chords cut each other, the product of the segment lengths of one of them is equal to the product of the segment lengths of the other. Here, one of the chords is a diameter. That is special in that it is the bisector of any chord it crosses at right angles. That means ...
x·x = 2·6
x = √12 = 2√3
2. Secants from an external point have the same product of measures to the near and far intersection points with the circle. Since there is only one intersection point with a tangent, the near and far lengths are the same.
4·(4+8) = x·x
x = √48 = 4√3
