Solve the proportion.
2 answers:
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Answer:
See explanation
Step-by-step explanation:
<u>Given:</u> ΔABC ≅ ΔDEF
AM, DN - medians
<u>Prove:</u> AM ≅ DN
Proof:
1. Congruent triangles ABC and DEF have congruent corresponding parts:
- AB ≅ DE;
- BC ≅ EF;
- ∠ABC ≅ ∠DEF.
2. BM ≅ MC - definition of the median AM;
3. EN ≅ NF - definition of the median DN;
4. AB ≅ 2BM, EF ≅ 2EN
BM ≅ 1/2 AB,
EN ≅ 1/2 EF,
thus, BM ≅ EN
5. Consider two triangles ABM and DEN. In these triangles \:
- AB ≅ DE (see 1));
- BM ≅ EN (see 4));
- ∠ABM ≅ ∠DEN (see 1).
So, ΔABM ≅ ΔDEN by SAS postulate.
6. Congruent triangles ABM and DEN have congruent corresponding sides BM and DN.
Answer:
5 a) PMT=$1,465.60
b) Total Payments=$527,616
c) Total Interest=$331,616
6a) Interest=$1,079.93
b) Principal=$584.07
Step-by-step explanation:
a. Given the loan amount is $196,000, annual rate is 8.2% and the loan term is 30 years.
-The monthly mortgage payment can be calculated as follows:
Where:
- PMT is the monthly mortgage payment
- r is the annual interest rate
- n,t is the number of annual payments and time in years respectively
-We substitute to solve for PMT:
Hence, the monthly mortgage payment is $1,465.60
b. The total number of payments is obtained by multiplying the total number of payments by the amount of each payment:
Hence, the total amount of payments is $527,616
c. The amount of interest paid over the loan's term is obtained by subtracting the principal loan amount from the total payments made:
Hence, an interest amount of $331,616 is paid over the loan's term.
6 a) We first obtain the effective loan amount by subtracting the down-payment:
The interest paid on the first mortgage payment is calculated as below:
Hence, the amount of interest in the first payment is $1,079.93
b. The amount of principal repaid is obtained by subtracting the interest amount from the monthly mortgage payments;
Hence, the amount of principal applied is $584.07