Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 7 Herrega kutaa 9: Walsimtiifi Walfakkii

Wanti fuula kana irra jiru hundi boqonnaa 7 kitaaba Herrega kutaa 9 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

4
Kaardii: 10
Gaaffii shaakalaa boqonnaa 7: 209–246
Fuula kitaabaa boqonnaa 7

Boqonnaan 7 maal haguuga

1.Revision on Congruency of Triangles
2.Definition of Similar Figures
3.Theorems on Similar Plane Figures
4.Ratio of Perimeters of Similar Plane Figures
5.Ratio of Areas of Similar Plane Figures
6.Construction of Similar Plane Figures
7.Applications on Similarities

Yaadannoo gabaabaa boqonnaa 7

Kaardiiwwan fuula Herrega kutaa 9 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

Garaagarummaa Scale Factor Sararaawaa fi AreaDogoggora baratame

Yoom akka itti fayyadamtu

Dheerinni cinaachaa yeroo jijjiiramu Perimeter fi Area akkamitti akka jijjiiramu gaaffilee gaafataman irratti ilaali.

Of eeggadhu

Dheerina cinaachaa 2n baay'isuun Perimeter dachaa taasisa, garuu Area 2^2 = 4n baay'isa.

Grade 9 Mathematics, fuula 209-246 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Reeshoo Area Bocaalee WalfakkaatooFoormulaa

\frac{A_1}{A_2} = \left(\frac{s_1}{s_2}\right)^2 = k^2

\frac{A_1}{A_2} = \left(\frac{s_1}{s_2}\right)^2 = k^2

$A_1$: Area boca walfakkaataa isa duraa $\text{m}^2$
$A_2$: Area boca walfakkaataa isa lammaffaa $\text{m}^2$
$s_1$: side length boca isa duraa $\text{m}$
$s_2$: side length walsimu boca isa lammaffaa $\text{m}$
$k$: faakterii iskeelii $1$

Yoom akka itti fayyadamtu

Dheerinni cinaachaa yookiin scale factor yoo kenname Area boca walfakkaataa shallaguuf fayyadami.

Of eeggadhu

Scale factor iskuweerii gochuu hin dagatin. Reeshoon Area k^2 dha malee k miti.

Grade 9 Mathematics, fuula 209-246 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Reeshoo Perimeter Bocaalee WalfakkaatooFoormulaa

\frac{P_1}{P_2} = \frac{s_1}{s_2} = k

\frac{P_1}{P_2} = \frac{s_1}{s_2} = k

$P_1$: Perimeter boca walfakkaataa isa duraa $\text{m}$
$P_2$: Perimeter boca walfakkaataa isa lammaffaa $\text{m}$
$s_1$: side length boca isa duraa $\text{m}$
$s_2$: side length walsimu boca isa lammaffaa $\text{m}$
$k$: faakterii iskeelii $1$

Yoom akka itti fayyadamtu

Bocoonni ji'omeetirii lama walfakkaatoo yoo ta'an Perimeter yookiin dheerina cinaachaa hin beekamne baruuf fayyadami.

Of eeggadhu

Reeshoo yeroo qindeessitu cinaachota walsiman qofa walitti heeri.

Grade 9 Mathematics, fuula 209-246 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Ulaagaalee Walfakkannoo Rog-sadootaaGabatee wabiiAA · SSS · SAS

Ulaagaa	Walqixxummaa yookiin Reeshoo	Goolaba
AA	$\angle A = \angle D \text{ and } \angle B = \angle E$	$\triangle ABC \sim \triangle DEF$
SSS	$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$	$\triangle ABC \sim \triangle DEF$
SAS	$\frac{AB}{DE} = \frac{AC}{DF} \text{ and } \angle A = \angle D$	$\triangle ABC \sim \triangle DEF$

Yoom akka itti fayyadamtu

Rog-sadoonni lama walfakkaatoo ta'uu isaanii ulaagaalee kofa yookiin cinaachaa muraasaan mirkaneessuuf fayyadami.

Of eeggadhu

Walfakkannoo SAS keessatti kofni walqixa ta'e cinaachota lamaan reeshoo qaban gidduu ta'uu qaba.

Grade 9 Mathematics, fuula 209-246 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 7

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

According to the AA (Angle-Angle) similarity theorem, two triangles are similar if:

A.Two angles of one triangle are congruent to two angles of the other triangle
B.All three pairs of corresponding sides are equal in length
C.The two triangles have exactly equal perimeters
D.The two triangles have equal areas

Deebii fi sababa agarsiisi

Deebii: A Two angles of one triangle are congruent to two angles of the other triangle

Sababa

The AA similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.

Gaaffii 2

The ratio of the perimeters of two similar triangles is 3:5. What is the ratio of their corresponding sides?

A.9:25
B.3:5
C.6:15
D.1:2

Deebii fi sababa agarsiisi

Deebii: B 3:5

Sababa

For any two similar plane figures, the ratio of their perimeters is equal to the ratio of their corresponding side lengths, which is 3:5.

Gaaffii 3

A giraffe is 6 m tall and casts a shadow of 4 m. At the same time, a smaller giraffe casts a shadow of 2 m. How tall is the smaller giraffe?

A.2 m
B.3 m
C.4 m
D.5 m

Deebii fi sababa agarsiisi

Deebii: B 3 m

Sababa

Using the proportionality of similar triangles: Height / Shadow = 6 / 4 = x / 2. Solving for x gives x = (6 * 2) / 4 = 3 m.

Gaaffii 4

If the ratio of the side lengths of two similar rectangles is 3:1, what is the ratio of their areas?

A.3:1
B.6:1
C.9:1
D.12:1

Deebii fi sababa agarsiisi

Deebii: C 9:1

Sababa

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides: 3² : 1² = 9:1.

Gaaffii 5

Given that ΔABC ~ ΔDEF, with AB = 9 cm, BC = 15 cm, and DE = 6 cm. What is the length of side EF?

A.8 cm
B.10 cm
C.12 cm
D.18 cm

Deebii fi sababa agarsiisi

Deebii: B 10 cm

Sababa

Because the triangles are similar, the ratios of corresponding sides are equal: AB / DE = BC / EF, which means 9 / 6 = 15 / EF. Therefore, EF = (15 * 6) / 9 = 10 cm.

Gaaffii 6

Two similar triangles have corresponding sides of length 3 cm and 9 cm. If the area of the smaller triangle is 12 cm², what is the area of the larger triangle?

A.36 cm2
B.72 cm2
C.108 cm2
D.144 cm2

Deebii fi sababa agarsiisi

Deebii: C 108 cm2

Sababa

The scale factor of side lengths is 9 / 3 = 3. The ratio of their areas is 3² = 9. Thus, the area of the larger triangle is 12 * 9 = 108 cm².

Gaaffii 7

In Hawassa, a flagpole casts a shadow 9 m long. At the same moment, a student who is 1.8 m tall standing nearby casts a shadow 4 m long. How tall is the flagpole?

A.3.60 m
B.4.05 m
C.4.50 m
D.5.20 m

Deebii fi sababa agarsiisi

Deebii: B 4.05 m

Sababa

Set up the proportion: Height / Shadow = 1.8 / 4 = h / 9. Solving for height gives h = (1.8 * 9) / 4 = 16.2 / 4 = 4.05 m.

Gaaffii 8

Two similar triangles have areas of 144 cm² and 169 cm². If a side of the larger triangle is 26 cm, what is the length of the corresponding side of the smaller triangle?

A.20 cm
B.22 cm
C.24 cm
D.25 cm

Deebii fi sababa agarsiisi

Deebii: C 24 cm

Sababa

The ratio of corresponding sides is the square root of the ratio of areas: √(144 / 169) = 12 / 13. The side of the smaller triangle is 26 * (12 / 13) = 24 cm.

Gaaffii 9

Abdi is 1.8 meters tall and casts a shadow of 2.4 meters. His younger brother casts a shadow of 2 meters at the same time. How tall is Abdi's brother?

A.1.2 meters
B.1.4 meters
C.1.5 meters
D.1.6 meters

Deebii fi sababa agarsiisi

Deebii: C 1.5 meters

Sababa

By similarity of triangles formed with the ground: Height / Shadow = 1.8 / 2.4 = h / 2. Solving for h gives h = (1.8 * 2) / 2.4 = 3.6 / 2.4 = 1.5 meters.

Gaaffii 10

A photograph measuring 4 cm wide and 5 cm long is enlarged to make a wall mural in a hall in Addis Ababa. If the mural is 120 cm wide, what is the length of the mural?