Answer:
The proof is explained below.
Step-by-step explanation:
Given m∠ADB = m∠CDB and AD ≅ DC
we have to prove that m∠BAC = m∠BCA and BD⊥ AC
In ΔADO and ΔCDO
∠OAD=∠OCD (∵ADC is an isosceles triangle)
AD=DC (∵Given)
∠ADO=∠CDO (∵Given)
By ASA rule, ΔADO≅ΔCDO
In ΔBAD and ΔBCD
AD=DC (∵ABC is an isosceles triangle)
∠ADB=∠CDB (∵Given)
DB=DB (∵common)
By ASA rule, ΔADB≅ΔCDB
Now, ΔADB≅ΔCDB and ΔADO≅ΔCDO
⇒ ΔADB-ΔADO≅ΔCDB-ΔCDO
⇒ ΔABO≅ΔCBO
Hence, by CPCT, m∠BAC = m∠BCA
Now, we have to prove that BD⊥ AC i.e we have to prove m∠BOA=90°
Now, ΔABO≅ΔCBO therefore by CPCT, m∠BOA = m∠BOC
But, m∠BOA + m∠BOC=180° (linear pair)
⇒ m∠BOA + m∠BOA=180°
⇒ 2m∠BOA=180° ⇒ m∠BOA=90°
Hence, BD⊥ AC
Answer:
x=70, which is D.
Step-by-step explanation:
As you can see, (2x-30) and x are different angles, but add up to 180. So, we can make an equation that looks like this:
(2x-30)+x=180
2x-30+x=180
3x=210
x=70
:)
Answer:
3<em>s</em>
Step-by-step explanation:
<u>Given:</u>
Jim is twice as old as his sister.
His sister's age is signified by the variable <em>s</em>.
∴ Jim's age is 2<em>s</em>.
You are trying to find the sum of both their ages, or add them together:
2<em>s</em> + <em>s</em>
Simplify. Combine like terms:
<em>2s </em>+<em> s</em> = 3<em>s</em>
3<em>s</em> is the expression you will use to find the sum of their ages.
3x + 4y = 17 (1)
-4x - 3y = -18 (2)
multiply equation (1) by 4 and equation (2) by 3 to eliminate x
(× 4) 12x + 16y = 68 (1)
(× 3) -12x - 9y = -54 (2)
---------------------------------------------Add
7y = 14
y = 2
Replace y = 2 into equation (1) 3x + 4y = 17 to find x
3x + 4(2)= 17
3x + 8 = 17
3x = 9
x = 3
Anwser:
(3,2)
Hope it helps
An event measured in days would be something long enough that to measure it in hours would be too big of a number. For example, the Olympics could be measured in days because it takes place over the course of several weeks, so keeping track of Day 1, Day 2, etc. would make more sense than counting by hours.
