Answer:
The two column proof can be presented as follows;
Statement 
Reason
1. RUST is a rectangle Given
2. RU = ST ; UT = RS Definition of a rectangle
3. ∠STU and ∠SRU are right angles Definition of a rectangle
4. ΔURS ≅ ΔSTU By SAS rule of congruency
5. ∠USR = ∠SUT By CPCTC
Step-by-step explanation:
Given that the side RU, the angle ∠SRU and the side RS of triangle ΔURS are congruent to the side ST the angle ∠STU and the side UT of triangle ΔSTU, then ΔURS is congruent to ΔSTU, by the Side-Angle-Side (SAS) rule of congruency
Therefore, we have that ∠USR ≅ ∠SUT and therefore, it can be shown that ∠USR = ∠SUT using the Congruent Parts of Congruent Triangle are Congruent (CPCTC) postulate.
Answer:
x = 20
Step-by-step explanation:
angle 2 and 3 are congruent, becaus they are alternate interior angles. So, 3x-10 = x+30, 2x = 40, x= 20.
<span>Their ratio bases off of 3:2. 3 representing the brother, 2 representing the sister.
I guess the way it works is that the brother is 1.5 times the sister's age, we can conclude that the sister's age can be represented by 'x' whereas the brother is represented as '1.5', together they ran a total of 300 yards, so we can use this to set up the problem:
</span>x + 1.5x = 300 - Now we add like terms:
2.5x = 300 - Divide.
<span>x = 120 - Of course upon adding that back in we just reroute back to only knowing how far they ran.
</span><span>The problem is this, we have no idea what the variable is to determine their ages, the ratio is 3:2, but... the only solutions I can think of are:
</span><span>If 10 yards = 1 Year of age(roughly) we have:
</span><span>18 = Brother
12 = Sister
If 20 yards = 1 Year of age(roughly) we have:
9 and 6.
</span><span>Regardless I can't say for certain what their ages are. :/</span>
1. a=2 b=-3
2.
3.x=10 y=14
4.
I'll do the rest in 5 mins
