Δ DUM Δ MAP
hypotenuse: 15 2y-3
short leg: 12 0.5x + 6
y = 9 ⇒ 2(9) - 3 = 18 - 3 = 15 Congruent with the hypotenuse of Δ DUM
x = 12 ⇒ 0.5(12) + 6 = 6 + 6 = 12 Congruent with the short leg of Δ DUM
SAS postulate states that two triangles are congruent if 2 of its sides and 1 angle have equal measure. Both the hypotenuse and short leg are equal in measure. Thus, both triangles are congruent with each other.
Answer: 8
Step-by-step explanation:
Since AB is a tangent, angle CAB is a right angle. Thus, by the Pythagorean theorem,
Answer:
Number : 42
Step-by-step explanation:
This number will be a two - digit number, and hence we can say that it is yz. The ratio of the units digit to the tens digit is given by 1 / 2, so z / y = 1 / 2.
In addition the tens digit is 2 more than the units digit, so y = z + 2. We therefore have the following system of equations,
y = z + 2,
z / y = 1 / 2
Substituting the first equation into the second we receive z / z + 2 = 1 / 2. Using this we can solve for z.
z / z + 2 = 1 / 2 ( Cross - Multiply )
z + 2 = 2z, z = 2
And knowing z we can solve for y. y = z + 2 = 2 + 2 = 4. Therefore our number is 42.
Answer:
x = 3
Step-by-step explanation:
Since ΔABC is isosceles with ∠A = 100° then the base angles are equal, that is
∠C = ∠B , that is
14x - 2 = 12x + 4 ( subtract 12x from both sides )
2x - 2 = 4 ( add 2 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3