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Triangles-HOTS Questions: Prove That The Segment QR - ST

The document contains 10 problems involving proofs of properties of triangles. The problems cover topics like congruence of triangles using angle-side-angle and side-side-side criteria, relationships between angles and sides of triangles, medians and chords of circles, and finding missing lengths and angle measures. Multiple choice questions test concepts like identifying corresponding parts of congruent triangles, applying triangle congruence rules, and finding angle measures based on given information.

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1K views3 pages

Triangles-HOTS Questions: Prove That The Segment QR - ST

The document contains 10 problems involving proofs of properties of triangles. The problems cover topics like congruence of triangles using angle-side-angle and side-side-side criteria, relationships between angles and sides of triangles, medians and chords of circles, and finding missing lengths and angle measures. Multiple choice questions test concepts like identifying corresponding parts of congruent triangles, applying triangle congruence rules, and finding angle measures based on given information.

Uploaded by

hkjhjhkj
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Triangles-HOTS Questions

1.  ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA. Prove that δABD ≌ ΔBAC.

2.  In the given figure, triangles PQC and PRC are such that QC = PR and PQ = CR. Prove that ∠PCQ = ∠CPR.

3.  In the given figure, AB = AD, AC = AE and ∠BAD = ∠EAC, then prove that BC = DE.

4.  ΔPQR is given and the sides QP and RP have been produced to S and T such that PQ = PS and PR = PT.
Prove that the segment QR || ST.
5.  In the given figure, AB = BC and ∠ABO = ∠CBO, then prove that ∠DAB = ∠ECB.

6.  In the given figure, AD is bisector of ∠BAC and ∠CPD = ∠BPD. Prove that ΔCAP ≌ ΔBAP.

7.  In the given figure, PS is median produced upto F and QE and RF are perpendiculars drawn from Q and R,
prove that QE = RF.

8.  In the given figure, equilateral ΔABD and ΔACE are drawn on the sides of a ΔABC. Prove that CD = BE.
9.  In given figure, RS is diameter and PQ chord of a circle with centre O. Prove that (a) ∠RPO = ∠OQR (b)
∠POQ = 2∠PRO

10.  In the given figure, T and M are two points inside a parallelogram PQRS such that PT = MR and PT || MR.
Then prove that
      (a) ΔPTR ≌ ΔRMP
      (b) RT || PM and RT = RM

Multiple Choice Questions


1.  Choose the correct statement
      (a) a triangle has two right angles
      (b) all the angles of a triangle are more than 60°
      (c) an exterior angle of a triangle is always greater than the opposite interior angles
      (d) all the angles of a triangle are less than 60°
2.  In two triangles, ABC and PQR, ∠A = 30°, ∠B = 70°, ∠P = 70°, ∠Q = 80° and AB = RP, then
      (a) ΔABC ≌ ΔPQR                              (b) ΔABC ≌ ΔQRP
      (c) ΔABC ≌ ΔRPQ                              (d) ΔABC ≌ ΔRQP
3.  In two triangles ABC and DEF, AB = DE, BC = DF and AC = EF, then
      (a) ΔABC ≌ ΔDEF                              (b) ΔABC Δ ΔEFD
      (c) ΔABC ≌ ΔFDE                              (d) none of these
4.  Are the given triangles congruent?

      (a) yes                              (b) no
      (c) can’t say
5.  If ΔABC is congruent to ΔDEF by SSS congruence rule, then:
      (a) ∠C < ∠F                              (b) ∠B < ∠E
      (c) ∠A < ∠D
      (d) ∠A = ∠D, ∠B = ∠E, ∠C = ∠F
6.  In the given figure, the congruency rule used in proving ∠ACD ≌ ∠ADB is
      (a) ASA                              (b) SAS
      (c) AAS                              (d) RHS
7.  Given two right angles triangles ABC and PRQ, such that ∠A = 20°, ∠Q = 20° and AC = QP. Write the
correspondence if triangles are congruent.
      (a) ΔABC≌ ΔPQR                              (b) ∠ABC ≌ ΔPRQ
      (c) ∠ABC ≌ ΔRQP                             (d) ΔABC ≌ ΔQRP
8.  In a triangle PQR if ∠QPR = 80° and PQ = PR, then ∠R and ∠Q are
      (a) 80°, 70°                              (b) 80°, 80°
      (c) 70°, 80°                              (d) 50°, 50°
9.  In the given figure, find PM

      (a) 3 cm                              (b) 5 cm
      (c) 4 cm                              (d) 2 cm
10.  In the given figure, AD is the median then ∠BAD is

      (a) 35°                                 (b) 70°


      (c) 110°                              (d) 55°

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