Advertisements
Advertisements
प्रश्न
In the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the mid-point of the line segments AB and PQ.
Advertisements
उत्तर
Since AP and BQ are perpendiculars to the line segment AB, therefore Ap and BQ are parallel to each other.
In ΔAOP and ΔBOQ
∠PAQ = ∠QBO = 90°
∠APO = ∠BQO ...(alternate angles)
AP = BQ
Therefore, ΔAOP ≅ ΔBOQ AOP BOQ ...(ASA criteria)
Hence, AO = OB and PO = OQ
Thus, O is the mid-point of the line segments AB and PQ.
APPEARS IN
संबंधित प्रश्न
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to ∠E
In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangles in each pair are congruent.
By ______ test
ΔPRQ ≅ ΔSTU
As shown in the following figure, in ΔLMN and ΔPNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.
On the sides AB and AC of triangle ABC, equilateral triangle ABD and ACE are drawn. Prove that:
- ∠CAD = ∠BAE
- CD = BE
In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.
ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent angles
If AB = QR, BC = PR and CA = PQ, then ______.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side AB of ∆ABC so that the two triangles are congruent? Give reason for your answer.
ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.
