What is the most detailed collection of geometry exercises for 8th-grade students? When do 8th-grade students in Vietnam achieve the "Excellent Student" title?

What is the most detailed collection of geometry exercises for 8th-grade students in Vietnam?

You may refer to the following most detailed collection of geometry exercises for 8th-grade students in Vietnam:

Most detailed collection of geometry exercises for 8th-grade students

Exercise 1: Given quadrilateral ABCD where the angles A; B; C; D are proportional to 5; 8; 13 and 10.

a/ Calculate the measures of the angles of quadrilateral ABCD.

b/ Extend sides AB and DC to meet at E, and extend sides AD and BC to meet at F. The bisectors of angles AED and AFB meet at O. The bisector of angle AFB intersects sides CD and AB at M and N, respectively. Prove that O is the midpoint of segment MN.

Exercise 2: Given trapezoid ABCD (AB // CD).

a/ Prove that if the bisectors of angles A and D both pass through the midpoint F of side BC, then side AD equals the sum of the two bases.

b/ Prove that if AD = AB + CD, then the bisectors of angles A and D intersect at the midpoint of side BC.

Exercise 3: Given rectangle ABCD. Draw AH perpendicular to BD. The midpoint of DH is I. Connect AI. Draw a line perpendicular to AI at I intersecting side BC at K. Prove that K is the midpoint of side BC.

Exercise 4: Given parallelogram ABCD, with diagonals intersecting at O. Lines d1 and d2 both passing through O are perpendicular to each other. Line d1 intersects sides AB and CD at M and P. Line d2 intersects sides BC and AD at N and Q.

a/ Prove that quadrilateral MNPQ is a rhombus.

b/ If ABCD is a square, what is quadrilateral MNPQ? Prove it.

Exercise 5: Given quadrilateral ABCD where AD = BC and AB < CD. The midpoints of sides AB and CD are M and N. The midpoints of diagonals BD and AC are P and Q.

a/ Prove that quadrilateral MNPQ is a rhombus.

b/ The extended sides DA and CB intersect at G, draw bisector Gx of angle AGB. Prove that Gx // MN.

II. Areas of Rectangle - Square - Triangle:

Exercise 1: Given rectangle ABCD with AB = 5cm, BC = 4cm. On side AD, construct triangle ADE such that AE and DE intersect side BC at M and N respectively, where M is the midpoint of segment AE. Calculate the area of triangle ADE.

Exercise 2:

1/ Calculate the area of a rectangle given that a point M in the rectangle is equidistant to three sides and the intersection of two diagonals, and that distance is 4cm.

2/ Calculate the area of a right trapezoid with the shorter base equal to the height, each measuring 6cm, and the largest angle being 135 degrees.

Exercise 3:

1/ Prove that the area of the square constructed on the leg of an isosceles right triangle equals twice the area of the square constructed on the altitude from the hypotenuse.

2/ Prove that the area of the square having a diagonal as its side in the rectangle is greater than or equal to twice the area of the rectangle.

Exercise 4: Given two squares with side length a sharing one vertex, with one square's side lying on the diagonal of the other square. Calculate the common area of the two squares.

III. Triangle Area:

Exercise 1:

1/ Given rectangle ABCD with AB = 4cm, BC = 3cm. On DC, take a point M so that MC = 2cm, with point N on side AB. Calculate the area of triangle CMN.

2/ Given rectangle ABCD and point M on side AB. Find the ratio SMCD / SABCD.

Exercise 2: Given triangle ABC. The medians BE and CF intersect at G. Compare the areas of triangle GEC and triangle ABC.

Exercise 3: Given trapezoid ABCD with BC // AD. The diagonals intersect at O. Prove that SOAB = SOCD and hence derive OA.OB = OC.OD.

Exercise 4:

a/ Prove that the medians of a triangle divide the triangle into 6 parts with equal areas.

b/ Let G be the centroid of triangle ABC then SGAB = SGAC = SGBC.

Exercise 5: Given right triangle ABC with the right angle at A. On sides AB, AC, BC, and outside the triangle, construct squares ABED, ACPQ, and BCMN. The altitude AH from the right triangle ABC intersects MN at F. Prove:

a/ SBHFN = SABED, hence AB^2 = BC.BH

b/ SHCMF = SACPQ, hence AC^2 = BC.HC

IV. Area of Trapezoid - Parallelogram - Rhombus

Exercise 1:

1/ Given rectangle ABCD with AB = 48cm, BC = 24cm, point E is the midpoint of DC. Find point F on AB such that the area of quadrilateral FBCE equals 1/3 the area of rectangle ABCD.

2/ The diagonals of a rhombus are 18 cm and 24 cm. Calculate the perimeter of the rhombus and the distance between the parallel sides.

Exercise 2: The area of a rhombus is 540 dm². One of its diagonals is 4.5 dm. Calculate the distance from the intersection of the diagonals to the sides.

Exercise 3:

a/ Calculate the area of an isosceles trapezoid with height h and diagonals perpendicular to each other.

b/ The diagonals of the isosceles trapezoid perpendicular to each other, and the sum of the two bases is 2a. Calculate the area of the trapezoid.

Exercise 4: Given parallelogram ABCD, on the extension of ray BA take point E, and on the extension of ray DA take point K. Line ED intersects KB at O. Prove that the areas of quadrilaterals ABOD and CEOK are equal.

V. Compilation 2:

Exercise 1: Given rectangle ABCD, with side AB = 4cm and BC = 3cm. Draw the internal angle bisectors, intersecting at M, N, P, Q.

a. Prove that triangle MNPQ is a square.

b. Calculate the area of square MNPQ.

Exercise 2: Given an equilateral triangle ABC.

a. Prove that the altitudes of this triangle are equal.

b. Prove that the sum of distances from any point D inside the equilateral triangle to the sides of the triangle does not depend on the position of D.

Exercise 3: Given isosceles triangle ABC with the vertex at A, and altitude AH, where O is the midpoint of AH. Ray BO intersects AC at D, ray CO intersects AB at E. Calculate the ratio of the area of quadrilateral ADOE to triangle ABC.

Exercise 4: Given parallelogram ABCD. From B, draw a line intersecting CD at M (M is between C and D). From D, draw a line intersecting CB at point N (N is between B and C). BM intersects DN at point I. It is known that MB = ND.

a. Prove the area of triangle ABM equals the area of triangle AND.

b. Prove that IA is the bisector of angle BID.

Note: The information is for reference purposes only./.

What is the most detailed collection of geometry exercises for 8th-grade students in Vietnam? When do 8th-grade students in Vietnam achieve the "Excellent Student" title? (Image from Internet)

When do 8th-grade students in Vietnam achieve the "Excellent Student" title?

Under point a, clause 1, Article 15 of Circular 22/2021/TT-BGDDT:

Commendations

1. Principals shall award certificates of achievement for students

a) End-of-year commendation

- Award the title “Học sinh Xuất sắc” (Excellent student) for students who have obtained Excellent training and learning results for the entire school year and achieved DTBmcn of at least 9.0 in subjects that are assessed via both feedback and scores.

- Award the title “Học sinh Giỏi” (Good student) for students who have obtained Excellent training and learning results for the entire school year.

b) Commend students for having unexpected merits in training and learning in the school year.

2. Students with special achievements shall be considered and requested for commendation by schools.

Under point a, clause 2, Article 9 of Circular 22/2021/TT-BGDDT:

Article 9. Assessment of learning results of students

...

2. Learning results in each semester and school year

For subjects assessed via both feedback and scores, DTBmhk is used to assess learning results of a student in each semester while DTBmcn is used to assess learning results of a student in the entire school year. Learning results of a student in each semester and in the entire school year shall be assessed by one of 4 categories: Excellent, Good, Qualified, Unqualified.

a) Excellent:

- All subjects assessed with feedback are placed in Qualified category.

- All subjects assessed by both feedback and scores have minimum scores of 6.5 for DTBmhk and DTBmcn with 6 subjects among which have minimum scores of 8.0 for DTBmhk and DTBmcn.

Thus. to achieve the "Excellent Student" title, 8th-grade students must have minimum scores of 6.5 for DTBmcn in all subjects with at least 6 subjects among which have minimum scores of 9.0 for DTBmcn.

Additionally, all subjects assessed with feedback are placed in the Qualified category, and the training results for the entire school year are assessed as Excellent.

What are the main goals of educating 8th-grade students in Vietnam?

Under Article 2 of the Education Law 2019, the main goals of educating 8th-grade students in Vietnam are as follows:

The goals of education are to educate the Vietnamese into comprehensively developed persons who possess ethics, knowledge, education, physical health, aesthetic sense and profession; to shape and cultivate one's dignity, civic qualifications and competence; to nurture one’s patriotism, national spirit, loyalty to the ideology of national independence and socialism; to develop potentials, creativity of each individual; to improve the people’s knowledge and manpower, to foster talents, satisfying the demands of the construction and defense of the Fatherland and international integration.