How to find if two acute / obtuse triangles are similar - ISEE Upper Level Quantitative Reasoning

Card 1 of 12

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 1211 left

Question

NOTE: Figures NOT drawn to scale.

Refer to the above two triangles.

$\Delta ABC \sim \Delta DEF ,AB = 25, DE = 20, AC = 20$

What is ?

Tap to reveal answer

Answer

Corresponding sides of similar triangle are proportional, so if

$\Delta ABC \sim \Delta DEF$ , then

$\frac{DF}{AC}$ = $\frac{DE}{AB}$

Substitute the known sidelengths, then solve for :

$\frac{DF}{20}$ = $\frac{20}{25}$

$$\frac{DF}{20}$\cdot 20= $\frac{20}{25}$\cdot 20$

$DF = $\frac{400}{25}$$

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is the perimeter of $\Delta DEF$ ?

Tap to reveal answer

Answer

By definition, since, $\Delta ABC \sim \Delta DEF$ , side lengths are in proportion.

So,

$\frac{DE}{AB}$= $\frac{DF}{AC}$

$$\frac{DE}{15}$= $\frac{36}{12}$ = 3$

$$\frac{DE}{15}$ \cdot 15 = 3\cdot 15$

$\frac{EF}{BC}$= $\frac{DF}{AC}$

$$\frac{EF}{21}$= $\frac{36}{12}$ = 3$

$$\frac{EF}{21}$ \cdot 21 = 3\cdot 21$

The perimeter of $\Delta DEF$ is

.

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is ?

Tap to reveal answer

Answer

By definition, since $\Delta ABC \sim \Delta DEF$ , all side lengths are in proportion.

$\frac{AC}{DF}$ = $\frac{AB}{DE}$

$\frac{AC}{66}$ = $\frac{15}{45}$

$\frac{AC}{66}$ = $\frac{1}{3}$

$AC = $\frac{1}{3}$ \cdot 66 = 22$

← Didn't Know|Knew It →

Question

NOTE: Figures NOT drawn to scale.

Refer to the above two triangles.

$\Delta ABC \sim \Delta DEF ,AB = 25, DE = 20, AC = 20$

What is ?

Tap to reveal answer

Answer

Corresponding sides of similar triangle are proportional, so if

$\Delta ABC \sim \Delta DEF$ , then

$\frac{DF}{AC}$ = $\frac{DE}{AB}$

Substitute the known sidelengths, then solve for :

$\frac{DF}{20}$ = $\frac{20}{25}$

$$\frac{DF}{20}$\cdot 20= $\frac{20}{25}$\cdot 20$

$DF = $\frac{400}{25}$$

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is the perimeter of $\Delta DEF$ ?

Tap to reveal answer

Answer

By definition, since, $\Delta ABC \sim \Delta DEF$ , side lengths are in proportion.

So,

$\frac{DE}{AB}$= $\frac{DF}{AC}$

$$\frac{DE}{15}$= $\frac{36}{12}$ = 3$

$$\frac{DE}{15}$ \cdot 15 = 3\cdot 15$

$\frac{EF}{BC}$= $\frac{DF}{AC}$

$$\frac{EF}{21}$= $\frac{36}{12}$ = 3$

$$\frac{EF}{21}$ \cdot 21 = 3\cdot 21$

The perimeter of $\Delta DEF$ is

.

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is ?

Tap to reveal answer

Answer

By definition, since $\Delta ABC \sim \Delta DEF$ , all side lengths are in proportion.

$\frac{AC}{DF}$ = $\frac{AB}{DE}$

$\frac{AC}{66}$ = $\frac{15}{45}$

$\frac{AC}{66}$ = $\frac{1}{3}$

$AC = $\frac{1}{3}$ \cdot 66 = 22$

← Didn't Know|Knew It →

Question

NOTE: Figures NOT drawn to scale.

Refer to the above two triangles.

$\Delta ABC \sim \Delta DEF ,AB = 25, DE = 20, AC = 20$

What is ?

Tap to reveal answer

Answer

Corresponding sides of similar triangle are proportional, so if

$\Delta ABC \sim \Delta DEF$ , then

$\frac{DF}{AC}$ = $\frac{DE}{AB}$

Substitute the known sidelengths, then solve for :

$\frac{DF}{20}$ = $\frac{20}{25}$

$$\frac{DF}{20}$\cdot 20= $\frac{20}{25}$\cdot 20$

$DF = $\frac{400}{25}$$

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is the perimeter of $\Delta DEF$ ?

Tap to reveal answer

Answer

By definition, since, $\Delta ABC \sim \Delta DEF$ , side lengths are in proportion.

So,

$\frac{DE}{AB}$= $\frac{DF}{AC}$

$$\frac{DE}{15}$= $\frac{36}{12}$ = 3$

$$\frac{DE}{15}$ \cdot 15 = 3\cdot 15$

$\frac{EF}{BC}$= $\frac{DF}{AC}$

$$\frac{EF}{21}$= $\frac{36}{12}$ = 3$

$$\frac{EF}{21}$ \cdot 21 = 3\cdot 21$

The perimeter of $\Delta DEF$ is

.

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is ?

Tap to reveal answer

Answer

By definition, since $\Delta ABC \sim \Delta DEF$ , all side lengths are in proportion.

$\frac{AC}{DF}$ = $\frac{AB}{DE}$

$\frac{AC}{66}$ = $\frac{15}{45}$

$\frac{AC}{66}$ = $\frac{1}{3}$

$AC = $\frac{1}{3}$ \cdot 66 = 22$

← Didn't Know|Knew It →

Question

NOTE: Figures NOT drawn to scale.

Refer to the above two triangles.

$\Delta ABC \sim \Delta DEF ,AB = 25, DE = 20, AC = 20$

What is ?

Tap to reveal answer

Answer

Corresponding sides of similar triangle are proportional, so if

$\Delta ABC \sim \Delta DEF$ , then

$\frac{DF}{AC}$ = $\frac{DE}{AB}$

Substitute the known sidelengths, then solve for :

$\frac{DF}{20}$ = $\frac{20}{25}$

$$\frac{DF}{20}$\cdot 20= $\frac{20}{25}$\cdot 20$

$DF = $\frac{400}{25}$$

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is the perimeter of $\Delta DEF$ ?

Tap to reveal answer

Answer

By definition, since, $\Delta ABC \sim \Delta DEF$ , side lengths are in proportion.

So,

$\frac{DE}{AB}$= $\frac{DF}{AC}$

$$\frac{DE}{15}$= $\frac{36}{12}$ = 3$

$$\frac{DE}{15}$ \cdot 15 = 3\cdot 15$

$\frac{EF}{BC}$= $\frac{DF}{AC}$

$$\frac{EF}{21}$= $\frac{36}{12}$ = 3$

$$\frac{EF}{21}$ \cdot 21 = 3\cdot 21$

The perimeter of $\Delta DEF$ is

.

← Didn't Know|Knew It →

Question

$\Delta ABC \sim \Delta DEF$

What is ?

Tap to reveal answer

Answer

By definition, since $\Delta ABC \sim \Delta DEF$ , all side lengths are in proportion.

$\frac{AC}{DF}$ = $\frac{AB}{DE}$

$\frac{AC}{66}$ = $\frac{15}{45}$

$\frac{AC}{66}$ = $\frac{1}{3}$

$AC = $\frac{1}{3}$ \cdot 66 = 22$

← Didn't Know|Knew It →

0

Knew It