جبر - كتاب الرياضيات - الصف 10 - الفصل 2 - المملكة العربية السعودية

الفصل 6 اختبار الفصل

حدد ما إذا كان المضلعان متشابهين أم لا في كل من السؤالين الآتيين، وإذا كانا كذلك، فاكتب عبارة التشابه ومعامل التشابه، وضح إجابتك.

السؤال 1: (referring to the instruction above)

السؤال 2: (referring to the instruction above)

أبراج: استعمل المعلومات الآتية لحل السؤالين الآتيين: في شنغهاي في الصين، شاهد سائح قمة البرج في مرآة موضوعة على الأرض ووجهها إلى أعلى.

جبر: أوجد قيمتي y, x في كل من السؤالين الآتيين، مقربًا إجابتك إلى أقرب عشر إذا كان ذلك ضروريًا.

السؤال 4: (referring to the instruction above)

السؤال 5: (referring to the instruction above)

جبر: MNP مثلث متطابق الأضلاع، محيطه 18b + 12a ، إذا كانت QR قطعة منصفة فيه، فما قيمة QR؟

جبر: ABC مثلث قائم الزاوية ومتطابق الضلعين، وطول وتره h، إذا كانت DE قطعة منصفة للوتر وأحد ضلعي القائمة فيه وطولها 4x ، فما محيط ABC؟

نماذج: لدى سالم نموذج لسيارة سباق حقيقية، إذا كان طول السيارة الحقيقية 10 ft و 6 in ، وطول النموذج 7 in ، فما معامل تشابه النموذج إلى السيارة الحقيقية؟

أوجد قيمة x في كل من السؤالين الآتيين:

السؤال 9: (referring to the instruction above)

السؤال 10: (referring to the instruction above)

جبر: أوجد كل طول مشار إليه في كل من السؤالين الآتيين: WZ, UZ

السؤال 11: (referring to the instruction above)

السؤال 12: (referring to the instruction above)

وزارة التعليم 111 الفصل 6 اختبار الفصل

الفصل 6 اختبار الفصل حدد ما إذا كان المضلعان متشابهين أم لا في كل من السؤالين الآتيين، وإذا كانا كذلك، فاكتب عبارة التشابه ومعامل التشابه، وضح إجابتك. --- SECTION: 1 --- السؤال 1: (referring to the instruction above) --- SECTION: 2 --- السؤال 2: (referring to the instruction above) --- SECTION: 3 --- أبراج: استعمل المعلومات الآتية لحل السؤالين الآتيين: في شنغهاي في الصين، شاهد سائح قمة البرج في مرآة موضوعة على الأرض ووجهها إلى أعلى. a. كم مترا ارتفاع البرج تقريبا؟ b. لماذا تكون طريقة الانعكاس في المرآة في هذه الحالة أفضل للقياس غير المباشر لارتفاع البرج من استعمال الظل؟ --- SECTION: جبر --- جبر: أوجد قيمتي y, x في كل من السؤالين الآتيين، مقربًا إجابتك إلى أقرب عشر إذا كان ذلك ضروريًا. --- SECTION: 4 --- السؤال 4: (referring to the instruction above) --- SECTION: 5 --- السؤال 5: (referring to the instruction above) --- SECTION: 6 --- جبر: MNP مثلث متطابق الأضلاع، محيطه 18b + 12a ، إذا كانت QR قطعة منصفة فيه، فما قيمة QR؟ --- SECTION: 7 --- جبر: ABC مثلث قائم الزاوية ومتطابق الضلعين، وطول وتره h، إذا كانت DE قطعة منصفة للوتر وأحد ضلعي القائمة فيه وطولها 4x ، فما محيط ABC؟ --- SECTION: 8 --- نماذج: لدى سالم نموذج لسيارة سباق حقيقية، إذا كان طول السيارة الحقيقية 10 ft و 6 in ، وطول النموذج 7 in ، فما معامل تشابه النموذج إلى السيارة الحقيقية؟ أوجد قيمة x في كل من السؤالين الآتيين: --- SECTION: 9 --- السؤال 9: (referring to the instruction above) --- SECTION: 10 --- السؤال 10: (referring to the instruction above) --- SECTION: جبر --- جبر: أوجد كل طول مشار إليه في كل من السؤالين الآتيين: WZ, UZ --- SECTION: 11 --- السؤال 11: (referring to the instruction above) WZ. أوجد الطول WZ UZ. أوجد الطول UZ --- SECTION: 12 --- السؤال 12: (referring to the instruction above) KL. أوجد الطول KL وزارة التعليم 111 الفصل 6 اختبار الفصل --- VISUAL CONTEXT --- **DIAGRAM**: Untitled Description: Two right-angled triangles, ΔXYZ and ΔABC, are shown. ΔXYZ is smaller and to the left of ΔABC. Data: ΔXYZ has side XY = 4, side YZ = 7, and angle Z is a right angle (90°). ΔABC has side AB = 14, side BC = 24.5, and angle C is a right angle (90°). Key Values: XY = 4, YZ = 7, ∠Z = 90°, AB = 14, BC = 24.5, ∠C = 90° Context: Used to determine if the triangles are similar and to find the similarity ratio. **DIAGRAM**: Untitled Description: Two rectangles, FGHT and QJRS, are shown. FGHT is smaller and to the left of QJRS. Data: Rectangle FGHT has side FG = 9 and side GH = 4. Rectangle QJRS has side QR = 21 and side RS = 10. All angles in both rectangles are right angles. Key Values: FG = 9, GH = 4, QR = 21, RS = 10, All angles = 90° Context: Used to determine if the rectangles are similar and to find the similarity ratio. **DIAGRAM**: Untitled Description: A diagram illustrating a person (point A) observing a tower (point E) in a mirror (at point C). The person stands upright (AB), the tower stands upright (DE), and the mirror is on the ground. This forms two similar right-angled triangles: ΔABC and ΔEDC. Data: The person's height (AB) is 1.92m. The distance from the person's feet to the mirror (BC) is 0.4m. The distance from the mirror to the base of the tower (CD) is 87.6m. The height of the tower (DE) is labeled as 'x m'. Angles at B and D are right angles. The angles of incidence and reflection at C are congruent, making ΔABC similar to ΔEDC. Key Values: AB = 1.92m, BC = 0.4m, CD = 87.6m, DE = x m, ∠B = 90°, ∠D = 90°, ∠ACB = ∠ECD Context: Used to calculate the height of the tower using similar triangles and properties of reflection. **DIAGRAM**: Untitled Description: A large triangle with a line segment parallel to its base, creating a smaller similar triangle. The parallel lines are indicated by arrows. The sides are divided proportionally. Data: The top segment of the left side is (5x - 8). The bottom segment of the left side is (4y - 7). The top segment of the right side is (3x + 11). The bottom segment of the right side is (2y - 1). The line segment connecting (5x-8) and (3x+11) is parallel to the base, indicated by arrows on the lines. Key Values: Left top segment = 5x - 8, Left bottom segment = 4y - 7, Right top segment = 3x + 11, Right bottom segment = 2y - 1, Parallel lines indicated by arrows Context: Used to find the values of x and y using the Triangle Proportionality Theorem or properties of similar triangles. **DIAGRAM**: Untitled Description: Three parallel lines are intersected by two transversals. The parallel lines are indicated by arrows. The segments cut by the parallel lines on the transversals are proportional. Data: On the left transversal, the top segment is (20y - 2) and the bottom segment is (5x + 8). On the right transversal, the top segment is (17y + 3) and the bottom segment is (21x). Hash marks indicate corresponding segments are proportional. Key Values: Left top segment = 20y - 2, Left bottom segment = 5x + 8, Right top segment = 17y + 3, Right bottom segment = 21x, Parallel lines indicated by arrows Context: Used to find the values of x and y using the properties of parallel lines and transversals (proportional segments). **DIAGRAM**: Untitled Description: Two right-angled triangles are shown, implied to be similar. They are oriented such that their right angles are at the bottom and one acute angle is marked as congruent. Data: The left triangle has a hypotenuse of 21 and one leg of 18. An acute angle is marked with a single arc, and a right angle is marked. The right triangle has a hypotenuse of 25 and one leg of x. An acute angle is marked with a single arc (congruent to the angle in the left triangle), and a right angle is marked. Key Values: Left triangle hypotenuse = 21, Left triangle leg = 18, Right triangle hypotenuse = 25, Right triangle leg = x, Congruent acute angles, Right angles Context: Used to find the value of x using similarity ratios between the two triangles. **DIAGRAM**: Untitled Description: Two isosceles triangles are shown, implied to be similar. Both triangles have their base angles marked as congruent. Data: The left triangle has a base length of 30 and a leg length of 26. Its two base angles are marked with single arcs. The right triangle has a base length of 40 and a leg length of x. Its two base angles are marked with single arcs (congruent to the angles in the left triangle). Key Values: Left triangle base = 30, Left triangle leg = 26, Right triangle base = 40, Right triangle leg = x, Congruent base angles Context: Used to find the value of x using similarity ratios between the two triangles. **DIAGRAM**: Untitled Description: A right-angled triangle WZY with an altitude WU drawn from the right angle W to the hypotenuse ZY. This creates three similar triangles: ΔWZY, ΔWUZ, and ΔWUY. Data: The vertex W is at the top, Z at the bottom left, and Y at the bottom right. Angle W is a right angle. Point U is on ZY such that WU is perpendicular to ZY (indicated by a right angle symbol at U). Side WZ has length (x + 7). Side WY has length 20. Altitude WU has length 12. Segment ZU has length (x + 1). Key Values: ∠W = 90°, WU ⊥ ZY, WZ = x + 7, WY = 20, WU = 12, ZU = x + 1 Context: Used to find lengths WZ and UZ using geometric mean theorems in right triangles. **DIAGRAM**: Untitled Description: A triangle KLJ with an altitude MP drawn from point M on KJ to LJ. Angle L is a right angle, making ΔKLJ a right triangle. MP is perpendicular to LJ. Data: Vertex K is at the top left, L at the bottom left (with a right angle symbol), and J at the bottom right. Point M is on KJ. Point P is on LJ such that MP is perpendicular to LJ (indicated by a right angle symbol at P). Side KL has a labeled length of 10.4. Segment LP has length 8. Segment PJ has length 10. Altitude MP has length 12. Segment KM has length 13. The question asks to find KL. Key Values: ∠L = 90°, MP ⊥ LJ, KL = 10.4, LP = 8, PJ = 10, MP = 12, KM = 13 Context: Used to find the length KL using geometric theorems related to right triangles and altitudes.