📋 المحتوى المنظم
📖 محتوى تعليمي مفصّل
مثال 5
نوع: محتوى تعليمي
مثال 5
الأوتار المتساوية البعد عن المركز
نوع: محتوى تعليمي
الأوتار المتساوية البعد عن المركز
نوع: محتوى تعليمي
جبر: في A إذا كان 22 = WX = XY ، فأوجد AB. بما أن الوترين WX, XY متطابقان، فإن بعديهما عن A متساويان. إذن: AB = AC بالتعويض 5x = 3x + 4 بالتبسيط x = 2 إذن 10 = (2) 5 = AB
تحقق من فهمك
نوع: محتوى تعليمي
تحقق من فهمك
نوع: QUESTION_HOMEWORK
5) في H إذا كان: 14 = RS ، 4 – 3x = PQ ، فأوجد قيمة x
نوع: محتوى تعليمي
يمكنك استعمال النظرية 8.4؛ لإيجاد النقطة التي تبعد مسافات متساوية عن ثلاث نقاط ليست على استقامة واحدة، أو لتعيين مركز دائرة غير معلومة المركز.
إنشاءات هندسية
نوع: محتوى تعليمي
إنشاءات هندسية
رسم الدائرة التي تمر بثلاث نقاط ليست على استقامة واحدة
نوع: محتوى تعليمي
رسم الدائرة التي تمر بثلاث نقاط ليست على استقامة واحدة
الخطوة 1
نوع: محتوى تعليمي
الخطوة 1: ارسم ثلاث نقاط C , B , A ليست على استقامة واحدة، ثم ارسم القطعتين المستقيمتين AB , BC .
الخطوة 2
نوع: محتوى تعليمي
الخطوة 2: أنشئ العمودين m , l المنصفين للقطعتين AB , BC . وسم نقطة تقاطعهما D .
الخطوة 3
نوع: محتوى تعليمي
الخطوة 3: المستقيمان m , l يحويان قطرين في الدائرة المارة بالنقاط الثلاث بحسب النظرية 8.4 ، ونقطة تقاطعهما هي مركز الدائرة. ضع رأس الفرجار عند النقطة D ، وارسم دائرة تمر بالنقاط C , B , A .
تأكد
نوع: محتوى تعليمي
تأكد
المثالان 1, 2
نوع: محتوى تعليمي
المثالان 1, 2
نوع: محتوى تعليمي
جبر: أوجد قيمة x في كل مما يأتي:
نوع: QUESTION_HOMEWORK
1.
نوع: QUESTION_HOMEWORK
2.
نوع: QUESTION_HOMEWORK
3.
المثالان 3, 4
نوع: محتوى تعليمي
المثالان 3, 4
نوع: QUESTION_HOMEWORK
في P ، إذا كان: 134° = mJLK ، فأوجد القياسات الآتية، مقربًا إجابتك إلى أقرب جزء من مئة إذا لزم ذلك.
نوع: METADATA
وزارة التعليم
نوع: METADATA
الدرس 3-8 الأقواس والأوتار 197
🔍 عناصر مرئية
Circle with chords WX and XY
A circle with center A. Two chords, WX and XY, are drawn within the circle. Perpendicular segments are drawn from the center A to each chord. The segment perpendicular to chord WX has a length labeled 5x. The segment perpendicular to chord XY has a length labeled 3x+4. Points B and C are on the chords, indicating the foot of the perpendiculars. Points W, X, Y are on the circle.
Circle with chords PQ and RS
A circle with center H. Two chords, PQ and RS, are drawn within the circle. Perpendicular segments are drawn from the center H to each chord. The segment perpendicular to chord PQ has a length labeled 8 (meeting at T). The segment perpendicular to chord RS also has a length labeled 8 (meeting at U). Points P, Q, R, S are on the circle.
Drawing three non-collinear points and segments
A diagram showing three distinct points, A, B, and C, that are not aligned on a single straight line. Straight line segments are drawn connecting A to B (segment AB) and B to C (segment BC).
Constructing perpendicular bisectors
A diagram showing three distinct points, A, B, and C, that are not aligned on a single straight line. Straight line segments AB and BC are drawn. Two lines, l and m, are drawn. Line l is the perpendicular bisector of segment AB. Line m is the perpendicular bisector of segment BC. Lines l and m intersect at point D. Construction arcs are visible for the bisectors.
Drawing the circle
A diagram showing three distinct points, A, B, and C, that are not aligned on a single straight line. Segments AB and BC are drawn. Perpendicular bisectors l and m of segments AB and BC, respectively, intersect at point D. A circle is drawn with its center at point D, and the circumference of this circle passes through all three points A, B, and C.
Circle with inscribed angle RST
A circle with points R, S, T on its circumference. An inscribed angle RST is shown, with its vertex at S. The measure of arc RT is given as 93°. The measure of angle RST is labeled x°. The center of the circle is implied but not explicitly marked.
Circle with chords FG and GH
A circle with points F, G, H on its circumference. Chord FG has a length of 4 units. Chord GH also has a length of 4 units. The measure of arc FH is given as 160°. An inscribed angle FGH is shown, with its vertex at G, and its measure is labeled x°. The center of the circle is implied but not explicitly marked.
Circle with parallel chords AB and CD
A circle with two parallel chords, AB and CD. Points A, B, C, D are on the circumference. The length of chord AB is labeled 5x. The length of chord CD is labeled 3x+6. The measure of arc AD is given as 127°. The center of the circle is implied but not explicitly marked.
Circle with chord JK and center P
A circle with center P. A chord JK is drawn. A segment PQ is drawn from the center P to the chord JK, such that PQ is perpendicular to JK, and Q is on JK. The length of PQ is 6 units. The radius PJ is 10 units. Points J, L, K, M are on the circumference. The measure of arc JLK is given as 134°. The diagram also shows a segment from P to L and P to M, but no specific values for them.
📄 النص الكامل للصفحة
--- SECTION: مثال 5 ---
مثال 5
--- SECTION: الأوتار المتساوية البعد عن المركز ---
الأوتار المتساوية البعد عن المركز
جبر: في A إذا كان 22 = WX = XY ، فأوجد AB. بما أن الوترين WX, XY متطابقان، فإن بعديهما عن A متساويان. إذن: AB = AC بالتعويض 5x = 3x + 4 بالتبسيط x = 2 إذن 10 = (2) 5 = AB
--- SECTION: تحقق من فهمك ---
تحقق من فهمك
5) في H إذا كان: 14 = RS ، 4 – 3x = PQ ، فأوجد قيمة x
يمكنك استعمال النظرية 8.4؛ لإيجاد النقطة التي تبعد مسافات متساوية عن ثلاث نقاط ليست على استقامة واحدة، أو لتعيين مركز دائرة غير معلومة المركز.
--- SECTION: إنشاءات هندسية ---
إنشاءات هندسية
--- SECTION: رسم الدائرة التي تمر بثلاث نقاط ليست على استقامة واحدة ---
رسم الدائرة التي تمر بثلاث نقاط ليست على استقامة واحدة
--- SECTION: الخطوة 1 ---
الخطوة 1: ارسم ثلاث نقاط C , B , A ليست على استقامة واحدة، ثم ارسم القطعتين المستقيمتين AB , BC .
--- SECTION: الخطوة 2 ---
الخطوة 2: أنشئ العمودين m , l المنصفين للقطعتين AB , BC . وسم نقطة تقاطعهما D .
--- SECTION: الخطوة 3 ---
الخطوة 3: المستقيمان m , l يحويان قطرين في الدائرة المارة بالنقاط الثلاث بحسب النظرية 8.4 ، ونقطة تقاطعهما هي مركز الدائرة. ضع رأس الفرجار عند النقطة D ، وارسم دائرة تمر بالنقاط C , B , A .
--- SECTION: تأكد ---
تأكد
--- SECTION: المثالان 1, 2 ---
المثالان 1, 2
جبر: أوجد قيمة x في كل مما يأتي:
1.
2.
3.
--- SECTION: المثالان 3, 4 ---
المثالان 3, 4
في P ، إذا كان: 134° = mJLK ، فأوجد القياسات الآتية، مقربًا إجابتك إلى أقرب جزء من مئة إذا لزم ذلك.
4. mJL
5. PQ
وزارة التعليم
الدرس 3-8 الأقواس والأوتار 197
--- VISUAL CONTEXT ---
**DIAGRAM**: Circle with chords WX and XY
Description: A circle with center A. Two chords, WX and XY, are drawn within the circle. Perpendicular segments are drawn from the center A to each chord. The segment perpendicular to chord WX has a length labeled 5x. The segment perpendicular to chord XY has a length labeled 3x+4. Points B and C are on the chords, indicating the foot of the perpendiculars. Points W, X, Y are on the circle.
Context: Illustrates the theorem that chords equidistant from the center are congruent. Used to solve for x or chord lengths.
**DIAGRAM**: Circle with chords PQ and RS
Description: A circle with center H. Two chords, PQ and RS, are drawn within the circle. Perpendicular segments are drawn from the center H to each chord. The segment perpendicular to chord PQ has a length labeled 8 (meeting at T). The segment perpendicular to chord RS also has a length labeled 8 (meeting at U). Points P, Q, R, S are on the circle.
Context: Applies the theorem that chords equidistant from the center are congruent. Used to solve for x or chord lengths.
**DIAGRAM**: Drawing three non-collinear points and segments
Description: A diagram showing three distinct points, A, B, and C, that are not aligned on a single straight line. Straight line segments are drawn connecting A to B (segment AB) and B to C (segment BC).
Context: First step in constructing a circle that passes through three non-collinear points.
**DIAGRAM**: Constructing perpendicular bisectors
Description: A diagram showing three distinct points, A, B, and C, that are not aligned on a single straight line. Straight line segments AB and BC are drawn. Two lines, l and m, are drawn. Line l is the perpendicular bisector of segment AB. Line m is the perpendicular bisector of segment BC. Lines l and m intersect at point D. Construction arcs are visible for the bisectors.
Context: Second step in constructing a circle that passes through three non-collinear points, identifying the center of the circle.
**DIAGRAM**: Drawing the circle
Description: A diagram showing three distinct points, A, B, and C, that are not aligned on a single straight line. Segments AB and BC are drawn. Perpendicular bisectors l and m of segments AB and BC, respectively, intersect at point D. A circle is drawn with its center at point D, and the circumference of this circle passes through all three points A, B, and C.
Context: Final step in constructing a circle that passes through three non-collinear points, demonstrating that the intersection of perpendicular bisectors is the circumcenter.
**DIAGRAM**: Circle with inscribed angle RST
Description: A circle with points R, S, T on its circumference. An inscribed angle RST is shown, with its vertex at S. The measure of arc RT is given as 93°. The measure of angle RST is labeled x°. The center of the circle is implied but not explicitly marked.
Context: Used to find the value of x based on the relationship between an inscribed angle and its intercepted arc.
**DIAGRAM**: Circle with chords FG and GH
Description: A circle with points F, G, H on its circumference. Chord FG has a length of 4 units. Chord GH also has a length of 4 units. The measure of arc FH is given as 160°. An inscribed angle FGH is shown, with its vertex at G, and its measure is labeled x°. The center of the circle is implied but not explicitly marked.
Context: Used to find the value of x based on the relationship between an inscribed angle and its intercepted arc, and properties of congruent chords.
**DIAGRAM**: Circle with parallel chords AB and CD
Description: A circle with two parallel chords, AB and CD. Points A, B, C, D are on the circumference. The length of chord AB is labeled 5x. The length of chord CD is labeled 3x+6. The measure of arc AD is given as 127°. The center of the circle is implied but not explicitly marked.
Context: Used to find the value of x based on properties of parallel chords and their intercepted arcs.
**DIAGRAM**: Circle with chord JK and center P
Description: A circle with center P. A chord JK is drawn. A segment PQ is drawn from the center P to the chord JK, such that PQ is perpendicular to JK, and Q is on JK. The length of PQ is 6 units. The radius PJ is 10 units. Points J, L, K, M are on the circumference. The measure of arc JLK is given as 134°. The diagram also shows a segment from P to L and P to M, but no specific values for them.
Context: Used to find lengths of segments (like PQ) and arc measures (like mJL) using properties of chords, radii, and arcs in a circle.