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ICSE Class 9 Geometry: triangles (congruency, mid-point theorem) — practice questions

Explore 28 free Geometry: triangles (congruency, mid-point theorem) questions in ICSE Class 9 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Geometry: triangles (congruency, mid-point theorem) questions and exercises with answers

Showing questions 1–28 of 28.

What must two geometric shapes share to be called congruent?Read the answer and worked solution →Congruence between point sets is preserved under which motions?Read the answer and worked solution →In Euclidean geometry, two line segments are congruent if they have:Read the answer and worked solution →Two planar angles are defined to be congruent if they have equal:Read the answer and worked solution →Which criterion establishes congruence using three equal pairs of sides?Read the answer and worked solution →In the SAS criterion, the equal angle must be located:Read the answer and worked solution →The angle-side-angle postulate is historically attributed to:Read the answer and worked solution →Why is AAS equivalent to ASA for triangle congruence?Read the answer and worked solution →Under the RHS criterion, right triangles must share one equal leg and:Read the answer and worked solution →What makes SSA invalid as a universal congruence test?Read the answer and worked solution →In planar geometry, the AAA condition guarantees:Read the answer and worked solution →In geometry proofs, the first two letters of CPCTC stand for:Read the answer and worked solution →In the generalisation CPCFC, the letter F stands for:Read the answer and worked solution →A segment connecting the midpoints of two triangle sides is:Read the answer and worked solution →By the midpoint theorem, the length of the join of two midpoints is:Read the answer and worked solution →A line through a side midpoint parallel to a second side will:Read the answer and worked solution →Partitioning triangle sides in any equal ratio generalises to the:Read the answer and worked solution →The triangle formed by joining the midpoints of all three sides is:Read the answer and worked solution →Into how many congruent triangles does a medial triangle divide one?Read the answer and worked solution →The interior angles of any triangle in Euclidean plane always add up to:Read the answer and worked solution →That triangle angles sum to 180° is logically equivalent to the:Read the answer and worked solution →An exterior angle of a triangle equals the sum of the two:Read the answer and worked solution →Taking one exterior angle at each triangle vertex, their sum is:Read the answer and worked solution →The centroid divides each triangle median from vertex to base in ratio:Read the answer and worked solution →Match each triangle congruence criterion with its conditions:Read the answer and worked solution →Match each geometric theorem on triangles with its conclusion:Read the answer and worked solution →Match each triangle inequality theorem with its rule:Read the answer and worked solution →Match each special point of concurrency in triangles with its definition:Read the answer and worked solution →

Worked practice questions

What must two geometric shapes share to be called congruent?

  1. Equal size and shape
  2. Equal area only
  3. Equal perimeter only
  4. Equal orientation
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Correct answer: A. Equal size and shape

Two geometric shapes are congruent when they have identical shape and size.

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Congruence between point sets is preserved under which motions?

  1. Shear motions
  2. Rigid motions
  3. Scaling factors
  4. Dilation maps
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Correct answer: B. Rigid motions

Congruence requires points to be related by rigid motions like rotations and translations.

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In Euclidean geometry, two line segments are congruent if they have:

  1. The same slope
  2. A common midpoint
  3. The same length
  4. Parallel vectors
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Correct answer: C. The same length

Two line segments are congruent precisely when their lengths are equal.

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