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Marina86 [1]
3 years ago
11

What are the postulates for congruent triangles

Mathematics
1 answer:
Delvig [45]3 years ago
7 0

Hi there!

There are 5 ways to find if two triangles are congruent :

SSS, SAS, ASA, AAS & HL

<u>1. SSS (Side, Side, Side)</u>

Means that we have two triangles with 3 sides equal.

⇒ If 3 sides of one triangle are equal to 3 sides of another triangle, the triangles are congruent.

<u>2. SAS (Side, Angle, Side)</u>

Means that we have two triangles where we know 2 sides and the included angle are equal.

⇒ If 2 sides and the includent angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

<u>3. ASA (Angle, Side, Angle)</u>

Means that we have two triangles where we know 2 angles and the included side are equal.

⇒ If 2 angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

<u>4. AAS (Angle, Angle, Side)</u>

Means thant we have two triangles where we know 2 angles and the non-included side are equal.

⇒ If 2 angles and the non-included side of one triangle are equal to the coresponding angles and side of another triangle, the triangles are congruent.

<u>5. HL (Hypotenuse, leg)</u>

** This one only applies to <em><u>right-angled triangles</u></em>.**

Hypotenuse: The longest side of a right-angled triangle.

Legs: The other 2 sides of the right-angled triangle.

Means we have two right-angled triangles with the same length of hypotenuse and the same length for one of the other 2 legs (it doesn't matter which leg since the triangles could be rotated).

⇒ If the hypotenuse and one leg of one right-angled triangles are equal to the corresponding hypotenuse and leg of another right-angled triangles, the two triangles are congruent.


There you go! I really hope this helped, if there's anything just let me know! :)

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Answer:

l(n) = 80n + 520

Step-by-step explanation:

From the information given in the  question, there is a relationship between the number of new policy sold, n, and earning, I

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           For 5 new policies, he earned $920.

The rate of change of IIya's earning with respect to number of new policy sales is

             m = \frac{dI}{dn}

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The linear equation for the relationship is;

             l(n) = mn + b

I(n) is Ilya’s weekly income which is a function of the number of new policies, n

m is the rate of change of I with respect to n

n is the number of new policies,

b is the intial function which is IIya's income when n equals zero

Recall, Ilya earns a commission of $80 for each policy sold during the week. (m = $80 per policy)

                 l(n) = 80n + b

To complete the relationship l, we need to calculate the initial value b.

For 3 new policies, he earned $760,

             760 = 80(3) + b

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             b = 760 - 520

             b = 520

The final equation is l(n) = 80n + 520

From the final equation, we can deduce that Ilya’s weekly salary is $520 and he earns an additional $80 commission for each new policy sold.

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