All categories

3 years ago

Which postulate or theorem proves that these two triangles are congruent?

Mathematics

2 answers:

swat323 years ago

4 0

ANSWER

postulate or theorem proves that these two triangles are congruent is option (C)

i.e AAS Congruence Theorem

Reason

AAS Congruence Theorem

In this theorem two angle and one sides of the two triangle are equal.

In ΔMNR and ΔQNP

∠MNR =∠ QNP

( Vertically opposite angle property )

∠RMN = ∠QPN

(Corresponding angle property)

RN = NQ

( As given in the diagram )

therefore

ΔMNR≅ Δ QNP

these triangle are congurent by the AAS Congruence Theorem.

Hence proved

kotegsom [21]3 years ago

4 0

Answer:

C) AAS Congruence Theorem

Step-by-step explanation:

The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

In this case the congruent angles are: M with P (shown in the figure) and N, which is equal in both triangles because two opposite angles are formed in the intersection of segments MP with RQ.

The congruent non-included sides are RN and NQ (shown in the figure).

You might be interested in

Choose the like term of - 3 xy form: A. -37 B. - 3 y z C. yx C. None of these

lawyer [7]

Answer:

Step-by-step explanation:

yx can be rearranged to xy

it's like saying 2 x 3 is the same as 3 x 2

xy or yx is the variable

6 0

2 years ago

Al factorizar el trinomio cuadrado perfecto, obtenemos el siguiente resultado: (que no se como resolver) xd algun pro que sepa r

PolarNik [594]

Answer:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

Step-by-step explanation:

Trinomio Cuadrado Perfecto

El producto notable llamado cuadrado de un binomio se expresa como:

$(a-b)^2=a^2-2ab+b^2$

Si se tiene un trinomio, es posible convertirlo en un cuadrado perfecto si cumple con las condiciones impuestas en la fórmula:

* El primer término es un cuadrado perfecto

* El último término es un cuadrado perfecto

* El segundo término es el doble del proudcto de los dos términos del binomio.

Tenemos la expresión:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle a=\sqrt{\frac{100}{81}m^8p^{12}q^{16}z^2}$

$\displaystyle a=\frac{10}{9}m^4p^{6}q^{8}z$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle b=\sqrt{\frac{1}{49}m^2p^2z^8$

$\displaystyle b=\frac{1}{7}mpz^4$

Nos cercioramos de que el término central es 2ab:

$\displaystyle 2ab=2\frac{10}{9}m^4p^{6}q^{8}z\frac{1}{7}mpz^4$

Operando:

$\displaystyle 2ab=\frac{20}{63}m^5p^7q^8z^5$

Una vez verificado, ahora podemos decir que:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

5 0

2 years ago

HELP ME W MY MATH IM BEGGINGM

wel

Answer:

Year 1: 164.87

Year 2: 169.88

Year 5: 185.86

Step-by-step explanation:

She is earning 3% interest per year that compounds once yearly.

3 0

2 years ago

A small garden measures 8 ft by 7 ft. A uniform border around the garden increases the total area to 110 ft 2. What is the width

Alik [6]

Answer: 3

Step-by-step explanation:

You can answer this question by using the equation

(8+x)(7+x)=110

The x represents the width, as we do not know the area. If you simplify the equation, it becomes 56+15x+x2=110.

If you move all the terms to the left side, and rearrange it, it can become x^2+15x-54=0

This can be simplified into (x-3)(x+18)=0

This equation makes it so that x is either 3 or -18. It is not possible for a width to be -18, so the width must be 3.

8 0

2 years ago

What is the value of x in the equation x – y = 30, when y = 15

Mekhanik [1.2K]

The answer is 45 because 45-15=30, therefore x=45.

6 0

3 years ago

Read 2 more answers