"Properties of Similar Triangles" PPT Courseware 2

Description

"Properties of Similar Triangles" PPT Courseware 2

1. The ratios of the corresponding heights, the ratios of the corresponding midlines, and the ratios of the corresponding angle bisectors of similar triangles are all equal to ________.

2. The ratio of the perimeters of similar triangles is _________.

3. The ratio of the areas of similar triangles is equal to ________.

1. (3 points) As shown in the figure, the electric lamp P is directly above the horizontal bar AB. The shadow of AB under the light is CD, AB∥CD, AB=2 m, CD=5 m, and the distance from point P to CD is 3 m. Then the distance from point P to AB is ()

A.56m

B.67m

C.65m

D.103m

2. (4 points) It is known that △ABC∽△A′B′C′, the corresponding midline ratio is 2:3, and the height on side BC is 53, then the height on side B′C′ is ________.

3. (6 points) As shown in the figure, in △ABC, DE∥BC, AH⊥BC are at point H, and AH intersects DE at point G. It is known that DE=10, BC=15, AG=12. Find the length of GH.

∵DE∥BC, ∴△ADE∽△ABC, ∵AH⊥BC,

∴AH⊥DE, ∴DE/BC=AG/AH, that is, 10/15=12/AH,

∴AH=18, ∴GH=18-12=6

6. (3 points) If two triangles are similar, and their largest sides are 6 cm and 8 cm respectively, and the sum of their perimeters is 35 cm, then the perimeter of the smaller triangle is ________.

7． (3 points) It is known that the similarity ratio between △ABC and △A′B′C′ is 1:2, the circumference of △ABC is 30 cm, and

The ratio of the three sides of △A′B′C′ is 4:5:6, then the longest side of △A′B′C′ is ()

A． 44 cm B. 40 cm

C. 36 cm D． 24cm

18. (10 points) As shown in the picture, student Ding Xuan walked from street lamp AC to street lamp BD at night. When he walked to point P, he found that the apex of his shadow behind him just touched the bottom of street lamp AC. When he walked forward 20m When arriving at point Q, I found that the top of his shadow in front of me just touched the bottom of the street lamp BD. It is known that Ding Xuan is 1.5m tall and the height of the two street lamps is 9m. What is the distance between the two street lamps?

18. Assume AP=xm, then AB=20+2x,

From similar triangles, we can get 1.59=x2x+20,

Solve to get x=5, ∴AB=30m

【Integrated use】

19． (12 points) As shown in the figure, in △ABC, BC>AC, point D is on BC, and DC=AC. The bisector of ∠ACB intersects AD at point F. Point E is the midpoint of AB and connects EF.

(1) Verify: EF∥BC;

(2) If the area of ​​the quadrilateral BDFE is 6, find the area of ​​△ABD.

19. (1) ∵CF bisects ∠ACB, DC=AC, ∴CF is the midline of △ACD, ∴point F is the midpoint of AD, ∵point E is the midpoint of AB, ∴EF∥BD, that is, EF∥BC

(2) From (1), we know that EF∥BD,

∴△AEF∽△ABD,

∴S△AEFS△ABD=(AE/AB)2. And ∵AE/AB=12, S△AEF=S△ABD-S quadrilateral BDFE=S△ABD-6,

∴S△ABD－6S△ABD=122, ∴S△ABD=8

Keywords: teaching courseware on the properties of similar triangles, download the mathematics PPT courseware for the first volume of the ninth grade of Hebei Education Edition, download the mathematics slide courseware for the ninth grade, download the PPT courseware on the properties of similar triangles, .PPT format;

For more information about the "Properties of Similar Triangles" PPT courseware, please click on the "Properties of Similar Triangles" ppt tab.

"Properties of Similar Triangles" PPT Courseware 3:

"Properties of Similar Triangles" PPT Courseware 3 Situation Introduction: Known: ABC∽A'B'C', according to the definition of similarity, what conclusions do we have? Viewed from corresponding sides: __________________ Viewed from corresponding angles: __________________ Two triangles..

"Properties of Similar Triangles" PPT courseware:

"Properties of Similar Triangles" PPT courseware Learning Objectives 1. Master the properties theorem of similar triangles. 2. Master the comprehensive application of the determination theorem and property theorem of similar triangles to solve problems. 3. Further experience the learning idea of ​​analogy. 4. Through similar properties...

"Properties of Similar Triangles" Similar PPT Courseware of Figures 3:

"Properties of Similar Triangles" Similarity of Figures PPT Courseware 3 Fill in the blanks: The _______ of two similar triangles are equal and _______ are proportional. The ratio of the corresponding heights of similar triangles, the ratio of the corresponding midlines of similar triangles, and the ratio of the corresponding angle bisectors of similar triangles are all equal to...

File Info

Update Time: 2024-09-05

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 1 industry PPT template

Preview