Given: AD ≅ BC and AD ∥ BC
Prove: ABCD is a parallelogram.
Statements Reasons
1. AD ≅ BC; AD ∥ BC 1. given
2. ∠CAD and ∠ACB are alternate interior ∠s 2. definition of alternate interior angles
3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent
4. AC ≅ AC 4. reflexive property
5. △CAD ≅ △ACB 5. SAS congruency theorem
6. AB ≅ CD 6. Corresponding Parts of Congruent triangles are Congruent (CPCTC)
7. ABCD is a parallelogram 7. parallelogram side theorem
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Answer:
100 : 250
Step-by-step explanation:
Sum the parts of the ratio, 2 + 5 = 7 parts
Divide the quantity by 7 to find the value of one part of the ratio.
350 ÷ 7 = 50 ← value of 1 part of the ratio, thus
2 parts = 2 × 50 = 100
5 parts = 5 × 50 = 250
350 = 100 : 250 in the ratio 2 : 5
Answer:
Step-by-step explanation:
By triangle theorem for similarity we have
AC||DE if and only if
the ratios
Option I:
Here we find the ratios are equal to 1/2
Hence parallel
OPtion 2:
Here we get both ratios equal to 2/3 Hence parallel
Option 3:
Here we get I ratio =2/5 and II ratio =4/7
Since the two are not equal we get not parallel
