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كويز تفاعلي: 10 Questions: Triangle Congruence Practice
This exercise focuses on determining the congruence of triangles using various theorems such as HL, LA, LL, HA, SSS, and SAS. Analyze the geometric markings on each pair of triangles to decide if sufficient information exists to prove congruence.
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للحصول على الإجابات الصحيحة والمضمونة، يُرجى الرجوع إلى المعلم أو المصدر الدراسي المعتمد.
Question 1
DB question no.: 1
Points: 1
Determine whether the pair of triangles is congruent. If yes, include the theorem that applies.
Explanation
The triangles are congruent by the Hypotenuse-Leg (HL) theorem because they are right triangles that share a common hypotenuse and have one pair of congruent legs.
Question 2
DB question no.: 2
Points: 1
Determine whether the pair of triangles is congruent. If yes, include the theorem that applies.
Explanation
The triangles are congruent by the Leg-Angle (LA) theorem as they have one pair of congruent legs and one pair of congruent acute angles.
Question 3
DB question no.: 3
Points: 1
Determine whether the pair of triangles is congruent. If yes, include the theorem that applies.
Explanation
The triangles are congruent by the Leg-Leg (LL) theorem because both corresponding legs in these right triangles are congruent.
Question 4
DB question no.: 4
Points: 1
Determine whether the pair of triangles is congruent. If yes, include the theorem that applies.
Explanation
There is not enough information to prove congruence because the marked congruent parts (angle and leg) do not correspond correctly between the two triangles.
Question 5
DB question no.: 5
Points: 1
Determine whether the pair of triangles is congruent. If yes, include the theorem that applies.
Explanation
The triangles are congruent by the Hypotenuse-Angle (HA) theorem as they have congruent hypotenuses and one pair of congruent acute angles.
Question 6
DB question no.: 6
Points: 1
Determine whether the pair of triangles is congruent. If yes, include the theorem that applies.
Explanation
There is not enough information; only one pair of legs is marked as congruent, which is insufficient to prove congruence in right triangles.
Question 7
DB question no.: 7
Points: 1
Explain whether there is enough information given in the figure to prove that the triangles are congruent using SSS or SAS.
Explanation
$\angle GLH$ and $\angle JLK$ are vertical angles, so they are congruent. Therefore, $\Delta GLH \cong \Delta JLK$ by the SAS Congruence Postulate.
Question 8
DB question no.: 8
Points: 1
Explain whether there is enough information given in the figure to prove that the triangles are congruent using SSS or SAS.
Explanation
It is not known whether $\overline{QT} \cong \overline{SR}$, so you cannot use SSS, and none of the angles are known to be congruent, so you cannot use SAS.
Question 9
DB question no.: 9
Points: 1
Explain whether there is enough information given in the figure to prove that the triangles are congruent using SSS or SAS.
Explanation
The triangles share the side $\overline{AC}$, so they have two pairs of congruent sides. The given congruent angles are included angles, so $\Delta ABC \cong \Delta CDA$ by SAS.
Question 10
DB question no.: 10
Points: 1
Explain whether there is enough information given in the figure to prove that the triangles are congruent using SSS or SAS.
Explanation
Both triangles must have three pairs of congruent angles from the Third Angles Theorem, but no side lengths are known. Angle-Angle-Angle (AAA) is not enough to prove congruence.
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