Triangles
CBSE Class 10 Mathematics · 99 board questions from this chapter; 98 listed below, 2023–2026
- It is given that ABC ∼ EDF. Which of the following is not true?2026
- In DEF, AB ∥ EF. The value of x is:2026
- Devansh proved that ABC ∼ PQR using SAS similarity criteria. If he found ∠ C=∠ R, then which of the following was proved true?2026
- In the given figure, DE ∥ BC. If AD/DB=1/3 and AC=6 cm, then length AE is2026
- If Δ ABC and Δ DEF are similar such that 2 AB=DE and BC=8 cm, then EF is equal to:2026
- In the given figure, OA × OB=OC × OD. Which of the following option is correct?2026
- Shown below are three triangles. The measures of two adjacent sides and included angle are given for each triangle: Which of…2026
- Equation of another line parallel to the line represented by 2 x-6 y=7 is:2026
- In triangles ABC and PQR, ∠ A=∠ Q and ∠ B=∠ R, then AB: AC is equal to:2026
- It is given that Δ ABC ∼ Δ QRP such that AB=9 cm, BC=5 cm and PR=2 cm. Length of side QR is:2026
- In the given figure Δ ABC is shown, in which DE ∥ BC. If AD=5 cm, DB=2 · 5 cm and DE=8 cm, then the length of BC is:2026
- In the given figure, Δ ABC is an equilateral triangle. AD is a median of the triangle joining the points A(0, (5 √3)/2), D(0,0).…2026
- In the given figure, Δ AHK ∼ Δ ABC. If AK=10 cm, BC=3 · 5 cm and HK=7 cm, find the length of AC. OR In the given figure, XY ∥ QR,…2026
- In Δ ABC, DE ∥ BC. If AD=x, DB=x-2, AE=x+2 and EC=x-1, then find the value of x. OR In the figure given above, Δ ABC ∼ Δ XYZ,…2026
- In Δ ABC, DE ∥ BC. If AD=x, DB=x-2, AE=x+2 and EC=x-1, then find the value of x. OR In the figure given above, Δ ABC ∼ Δ XYZ,…2026
- In the given figure, Δ AHK ∼ Δ ABC. If AK=10 cm, BC=3 · 5 cm and HK=7 cm, find the length of AC. OR In the given figure, XY ∥ QR,…2026
- In the given figure, DE ∥ AC and DF ∥ AE. Prove that: BF/FE=BE/EC.2026
- Two right triangles PRQ and PSQ are drawn on the same hypotenuse PQ. If PR and QS intersect at T, prove that ST × TQ=PT × TR.2026
- In the given figure, Δ ABE ≅ Δ ACD. Prove that Δ ADE ∼ Δ ABC.2026
- D is a point on the side BC of ABC such that ∠ CAB=∠ CDA. Show that CA^2=CB × CD.2026
- In the given figure, DEFG is a square. ABC is right angle triangle with ∠ A=90^°. Prove that AG × DG=AF × DB.2026
- In the given figure, AB ∥ DE and AC ∥ DF. Show that ABC ∼ DEF. If BC=10 cm, EB=CF=5 cm and AB=7 cm, then find the length DE.2026
- The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/OC=BO/OD. Show that quadrilateral ABCD is…2026
- D is the mid-point of side BC of ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD=DG. Prove that…2026
- State and prove Basic Proportionality Theorem. OR In the given figure, CM and RN are respectively the medians of ABC and PQR. If…2026
- D is the mid-point of side BC of ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD=DG. Prove that…2026
- In Δ ABC, AD is a median. X is a point on AD such that AX: XD=2: 3. BX is extended so that it intersects AC at Y. Prove that BX=4…2026
- State and prove Basic Proportionality Theorem. OR In the given figure, CM and RN are respectively the medians of Δ ABC and Δ PQR.…2026
- Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the…2026
- D is the mid-point of side BC of ABC. CE and BF intersect at O, a point on AD. AD is produced to G such that OD=DG. Prove that…2026
- State and prove Basic Proportionality Theorem. OR In the given figure, CM and RN are respectively the medians of Δ ABC and Δ PQR.…2026
- In the adjoining figure, PQ∥XY∥ BC, AP=2 cm, PX=1.5 cm and BX=4 cm. If QY=0.75 cm, then AQ+CY=2025
- Given ABC ∼ PQR, ∠ A=30^° and ∠ Q=90^°. The value of (∠ R+∠ B) is2025
- ABC and PQR are shown in the adjoining figures. The measure of ∠ C is:2025
- In triangles ABC and DEF, ∠ B=∠ E, ∠ F=∠ C and AB=3 DE. Then, the two triangles are:2025
- Which of the following statements is false?2025
- In the given figure, PQ ∥ BC. If AP/PB=4/13 and AC=20 · 4 cm, then the length of AQ is:2025
- Which of the following statements is incorrect?2025
- In the adjoining figure, ABCD is a trapezium in which XY∥AB∥ CD. If AX=2/3 AD, then CY: YB=2025
- If in two triangles DEF and PQR, ∠ D=∠ Q and ∠ R=∠ E, then which of the following is not true?2025
- The measurements of Δ LMN and Δ ABC are shown in the figure given below. The length of side AC is:2025
- E and F are points on the sides AB and AC respectively of a ABC such that AE/EB=AF/FC=1/2. Which of the following relation is…2025
- In the given figure, in Δ ABC, AD ⊥ BC and ∠ BAC=90^°. If BC=16 cm and DC=4 cm, then the value of x is:2025
- In the adjoining figure, AD/BD=AE/EC and ∠ BDE=∠ CED, prove that ABC is an isosceles triangle.2025
- AD and PS are angle bisectors of ∠ A and ∠ P of triangles ABC and PQR. If ABC ∼ PQR, prove that ACD ∼ PRS.2025
- In ABC and PQR, AD and PS are altitudes such that ABD ∼ PQS and ACD ∼ PRS. Prove that ABC ∼ PQR.2025
- In the adjoining figure, AP=1 cm, BP=2 cm, AQ=1.5 cm and AC=4.5 cm. Prove that APQ ∼ ABC. Hence find the length of PQ, if BC=3.6…2025
- In the given figure, D is a point on the side BC of Δ ABC such that ∠ ADC=∠ BAC. Show that CA^2=CD. CB. OR In the given figure,…2025
- If ABC ∼ PQR in which AB=6 cm, BC=4 cm, AC=8 cm and PR=6 cm, then find the length of ( PQ+QR ). OR In the given figure,…2025
- P is a point on the side BC of ABC such that ∠ APC=∠ BAC. Prove that AC^2=BC · CP.2025
- AD and PS are medians of triangles ABC and PQR respectively such that ABD ∼ PQS. Prove that ABC ∼ PQR.2025
- In the given figure, PS/SQ=PT/TR and ∠ PST=∠ PRQ. Prove that Δ PQR is an isosceles triangle. OR In the given figure, Δ ABE ≅ Δ…2025
- State the basic proportionality theorem. Use the theorem to do the following: In ABC, AD is the angle bisector of angle A. BA is…2025
- The perimeter of an isosceles triangle is 32 cm. If each equal side is 5/6 th of the base, find the area of the triangle.2025
- If a line drawn parallel to one side of triangle intersecting the other two sides in distinct points divides the two sides in the…2025
- The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove…2025
- The corresponding sides of ABC and PQR are in the ratio 3: 5. AD ⊥ BC and PS ⊥ QR as shown in the following figures: (i) Prove…2025
- State the converse of basic proportionality theorem. Also find BF/FC in the following figure, given that AB∥DC∥ EF and AE/ED=2/3.…2025
- Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides the other…2025
- In the given figure, PA, QB and RC are perpendicular to AC. If PA=x units, QB=y units and RC=z units, prove that 1/x+1/z=1/y. OR…2025
- In the given figure ABC is shown. DE is parallel to BC. If AD=5 cm, DB=2.5 cm and BC=12 cm, then DE is equal to2024
- The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ / AB is equal to2024
- In Δ ABC, DE ∥ BC (as shown in the figure). If AD=2 cm, BD=3 cm, BC=7.5 cm, then the length of DE (in cm) is:2024
- In Δ ABC, DE ∥ BC (as shown in the figure). If AD=4 cm, AB=9 cm and AC=13 · 5 cm, then the length of EC is:2024
- In the given figure, in Δ ABC, DE ∥ BC. If AD=2 · 4 cm, DB=4 cm and AE=2 cm, then the length of AC is:2024
- Assertion (A): ABCD is a trapezium with DC ∥ AB. E and F are points on AD and BC respectively, such that EF ∥ AB. Then…2024
- Diagonals AC and BD of a trapezium ABCD intersect at O, where AB ∥ DC. If DO/OB=1/2, then show that AB=2 CD2024
- In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that:2024
- In the given figure, EA/EC=EB/ED, prove that Δ EAB ∼ Δ ECD2024
- In the given figure, EA/EC=EB/ED, prove that Δ EAB ∼ Δ ECD This section consists of 6 questions of 3 marks each.2024
- In ABC, altitudes AD and BE are drawn. If AD=7 cm, BE=9 cm and EC=12 cm then, find the length of CD.2024
- In the given figure, Δ AHK ∼ Δ ABC. If AK=8 cm, BC=3 · 2 cm and HK=6 · 4 cm, then find the length of AC.2024
- E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE ∼ Δ CFB. OR Sides AB, BC…2024
- State and prove Basic Proportionality theorem.2024
- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the…2024
- In the given figure, Δ FEC ≅ GDB and ∠ 1=∠ 2. Prove that Δ ADE ∼ Δ ABC. OR Sides AB and AC and median AD of a ABC are…2024
- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the…2024
- If Δ ABC ∼ Δ PQR with ∠ A=32^° and ∠ R=65^°, then the measure of ∠ B is:2023
- In ABC, PQ ∥ BC. If PB=6 cm, AP=4 cm, AQ=8 cm, find the length of AC.2023
- In the given figure, DE ∥ BC. The value of x is:2023
- In the given figure, ∠ A=∠ C, AB=6 cm, AP=12 cm, CP=4 cm. Then length of CD is:2023
- If PQR ∼ ABC; PQ=6 cm, AB=8 cm and the perimeter of ABC is 36 cm, then the perimeter of PQR is2023
- In the given figure, DE ∥ BC. If AD=3 cm, AB=7 cm and EC=3 cm, then the length of AE is2023
- In the given figure, DE ∥ BC. If AD=2 units, DB=AE=3 units and EC=x units, then the value of x is:2023
- In Δ ABC and Δ DEF, AB/DE=BC/FD. Which of the following makes the two triangles similar?2023
- In ABC, PQ ∥ BC. If PB=6 cm, AP=4 cm, AQ=8 cm, find the length of AC.2023
- In the given figure, PQ ∥ AC. If BP=4 cm, AP=2.4 cm and BQ=5 cm, then length of BC is:2023
- In the given figure, XZ is parallel to BC. AZ=3 cm, ZC=2 cm, BM=3 cm and MC=5 cm. Find the length of XY.2023
- In the given figure, ABC is a triangle in which DE ∥ BC. If AD=x, DB=x-2, AE=x+2 and EC=x-1, then find the value of x. OR…2023
- In the given figure, E is a point on the side CB produced of an isosceles triangle ABC with AB=AC. If AD ⊥ BC and EF ⊥ AC, then…2023
- Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with…2023
- In a PQR, N is a point on PR, such that QN ⊥ PR. If PN × NR=QN^2, prove that ∠ PQR=90^°. OR In the given figure, ABC and Δ DBC…2023
- If a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, prove that the other…2023
- D is a point on the side BC of a triangle ABC such that ∠ ADC=∠ BAC, prove that CA^2=CB. CD OR If AD and PM are medians of…2023
- Sides AB and AC and median AM of a ABC are proportional to sides DE and DF and Median DN of another DEF. Show that ABC ∼ DEF.…2023
- PA, QB and RC are each perpendicular to AC. If AP=x, QB=z, RC=y, AB=a and BC=b, then prove that 1/x+1/y=1/z. OR In the given…2023
- In the given figure, ∠ ADC=∠ BCA; prove that Δ ACB ∼ Δ ADC. Hence find BD if AC=8 cm and AD=3 cm. OR If a line is drawn parallel…2023
- Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of Δ PQR. Show…2023
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