Triangle congruence theorems are essential tools in geometry for determining if two triangles are identical in shape and size. The most common theorems include SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side). ASA requires two angles and the included side, while AAS requires two angles and a non-included side. Understanding these criteria helps in solving complex geometric proofs and calculating missing dimensions in figures.
رقم الاختبار983
الصفالصف التاسع المتقدم
المادةرياضيات
الفصلالفصل الثالث
السنة الدراسية2025/2026
عدد الأسئلة5
إجمالي النقاط5
تاريخ الإضافة2026-04-23
الزيارات7
المعلم أو الناشرMaya Dayoub
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Question 1
Points: 1
What is the reason these triangles are congruent?
Explanation
The triangles have two pairs of congruent angles and one pair of non-included congruent sides, which satisfies the AAS (Angle-Angle-Side) congruence theorem.
Question 2
Points: 1
State if the triangles are congruent and why.
Explanation
Only one pair of sides is marked congruent, and the vertical angles are congruent. This provides only one side and one angle (SA), which is insufficient to prove congruence.
Question 3
Points: 1
What is the measure of angle 2?
Explanation
The triangle is isosceles because two sides are marked congruent, meaning the base angles are equal (\(65^{\circ}\) each). The sum of angles in a triangle is \(180^{\circ}\), so angle 2 is \(180 - (65 + 65) = 50\).
Question 4
Points: 1
What is the length of BC?
Explanation
Based on the provided answer key, the sides \(AC\) and \(BC\) are treated as equal. Setting \(6x - 5 = 4x + 7\) gives \(2x = 12\), so \(x = 6\). Substituting into the expression for \(BC\): \(4(6) + 7 = 31\).
Question 5
Points: 1
Which of the following statements is NOT true if \(\Delta JKL\) is congruent to \(\Delta RST\)?
Explanation
In congruent triangles, corresponding parts must match based on the order of vertices. For \(\Delta JKL \cong \Delta RST\), \(K\) corresponds to \(S\), so \(\angle K \cong \angle S\). Thus, \(\angle K \cong \angle T\) is false.
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