Advertisements
Advertisements
Question
If in triangles ABC and DEF, `(AB)/(DE) = (BC)/(FD)`, then they will be similar, when ______.
Options
∠B = ∠E
∠A = ∠D
∠B = ∠D
∠A = ∠F
Solution
If in triangles ABC and DEF, `(AB)/(DE) = (BC)/(FD)`, then they will be similar, when ∠B = ∠D.
Explanation:
Given, in ∆ABC and ∆EDF,
`("AB")/("DE") = ("BC")/("FD")`
So, ∆ABC ~ ∆EDF if ∠B = ∠D ...[By SAS similarity criterion]
RELATED QUESTIONS
State which pair of triangles in the following figure are similar. Write the similarity criterion used by you for answering the question, and also write the pairs of similar triangles in the symbolic form:
CD and GH are, respectively, the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG, respectively. If ΔABC ~ ΔFEG, Show that
- `("CD")/("GH") = ("AC")/("FG")`
- ΔDCB ~ ΔHGE
- ΔDCA ~ ΔHGF
The sides of certain triangles are given below. Determine which of them right triangles are.
(a – 1) cm, `2sqrta` cm, (a + 1) cm
If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?
In a ∆PQR, PR2 – PQ2 = QR2 and M is a point on side PR such that QM ⊥ PR. Prove that QM2 = PM × MR.
In figure, if ∠1 = ∠2 and ΔNSQ ≅ ΔMTR, then prove that ΔPTS ~ ΔPRQ.
In figure, if DE || BC, find the ratio of ar(ADE) and ar(DECB).
In the figure, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD.
If in two triangles ABC and PQR, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ______.
In the given figure, ∠ADC = ∠BCA; prove that ΔACB ∼ ΔADC. Hence find BD if AC = 8 cm and AD = 3 cm.
