Advertisements
Advertisements
प्रश्न
In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P. Show that:
ΔAEP ∼ ΔADB
उत्तर
In ΔAEP and ΔADB,
∠AEP = ∠ADB ...(Each 90°)
∠PAE = ∠DAB ...(Common)
Hence, by using AA similarity criterion,
ΔAEP ∼ ΔADB
APPEARS IN
संबंधित प्रश्न
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:
In the following figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB.
In the following figure, `("QR")/("QS") = ("QT")/("PR")` and ∠1 = ∠2. Show that ΔPQS ~ ΔTQR.
S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ∼ ΔRTS.
State the two properties which are necessary for given two triangles to be similar.
In the given figure, seg AC and seg BD intersect each other in point P and `"AP"/"CP" = "BP"/"DP"`. Prove that, ∆ABP ~ ∆CDP.
In the given figure, value of x(in cm) is
If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?
In triangle PQR and MST, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Is ∆QPR ~ ∆TSM? Why?
Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?
If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ∆ABC.
It is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.
If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?
In figure, if ∠D = ∠C, then it is true that ΔADE ~ ΔACB? Why?
In the given figure, ΔLMN is similar to ΔPQR. To find the measure of ∠N, complete the following activity.
Given: ΔLMN ∼ ΔPQR
Since ΔLMN ∼ ΔPQR, therefore, corresponding angles are equal.
So, ∠L ≅ `square`
⇒ ∠L = `square`
We know, the sum of angles of a triangle = `square`
∴ ∠L + ∠M + ∠N = `square`
Substituting the values of ∠L and ∠M in equation (i),
`square` + `square` + ∠N = `square`
∠N + `square` = `square`
∠N = `square` – `square`
∠N = `square`
Hence, the measure of ∠N is `square`.
In the given figure, S is a point on side QR of ΔPQR such that ∠QPR = ∠PSR. Use this information to prove that PR2 = QR × SR.
In ΔABC, AP ⊥ BC, BQ ⊥ AC. If AP = 7, BQ = 8 and BC = 12, then find AC.
If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?
