Mathematics, 27.06.2019 06:00, davi113001

Which pairs of triangles can be shown to be congruent using rigid motions? select congruent or not congruent for each pair of triangles.

Answers: 2

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answered: yariiixox

Not Congruent

Not congruent

Congruent

Not congruent

answered: Aubreigh29

Congruent; Not Congruent; Congruent; Not Congruent; Not Congruent; Congruent

Step-by-step explanation:

We will use the distance formula to find the length of each segment:

$AB=\sqrt{(-4--3)^2+(4-2)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\BC=\sqrt{(-3--1)^2+(4-1)^2}=\sqrt{(-2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\AC=\sqrt{(2-1)^2+(-4--1)^2}=\sqrt{(1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}$

In order for ABC to be congruent to DEF, AB must be congruent to DE, BC must be congruent to EF, and AC must be congruent to DF:

$DE=\sqrt{(4-3)^2+(-2--4)^2}=\sqrt{(1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\EF=\sqrt{(3-1)^2+(-4--1)^2}=\sqrt{(2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}\\\\DF=\sqrt{(4-1)^2+(-2--1)^2}=\sqrt{(3)^2+(-1)^2}=\sqrt{9+1}=\sqrt{10}$

Since AB is congruent to DE, BC is congruent to EF and AC is congruent to DF, the two triangles are congruent.

In order for ABC to be congruent to JKL, AB must be congruent to JK, BC must be congruent to KL, and AC must be congruent to JL. We know the measurements of AB, BC and AC;

$JK=\sqrt{(-4--2)^2+(-1--3)^2}=\sqrt{(-2)^2+(2)^2}=\sqrt{4+4}=\sqrt{8}\\\\KL=\sqrt{(-2--1)^2+(-3-0)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}\\\\JL=\sqrt{(-1--4)^2+(0--1)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}$

While AC is congruent to JL, the other two corresponding pairs of sides are not congruent. Therefore the triangles are not congruent.

In order for ABC to be congruent to QRS, AB must be congruent to QR, BC must be congruent to RS, and AC must be congruent to QS. We know the measurements of AB, BC and AC;

$QR=\sqrt{(3-4)^2+(3-1)^2}=\sqrt{(-1)^2+(2)^2}=\sqrt{1+4}=\sqrt{5}\\\\RS=\sqrt{(3-1)^2+(3-0)^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}\\\\QS=\sqrt{(4-1)^2+(1-0)^2}=\sqrt{(3)^2+(1)^2}=\sqrt{9+1}=\sqrt{10}$

Since AB is congruent to QR, BC is congruent to RS, and AC is congruent to QS, this means that the two triangles are congruent.

Since ABC is congruent to DEF, and ABC is not congruent to JKL, this means that triangle DEF is not congruent to triangle JKL.

Since ABC is congruent to QRS, and QRS is not congruent to JKL, this means that triangle QRS is not congruent to JKL.

Since ABC is congruent to DEF and ABC is congruent to QRS, this means that DEF is congruent to QRS by the transitive property.

answered: Guest

ab: 2 n83b8eb7ebi. 8e yen in

answered: Guest

answer set (b) 0.5, 3/4 80% is in order from least to greatest.

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form. typically, the best form in which to evaluate rational numbers is in decimals. in order to convert a percent to a decimal, you would divide the given percentage by 100. you can also accomplish the conversion by moving the decimal point over two places to the left. for example, the decimal value of 80% is 80/100, or 0.8. in order to convert a fraction to a decimal, you need to divide the numerator by the denominator. for example, 3/4 is 0.75. so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.