1003076802
Level:
A
If the orthocenter of a triangle lies outside the triangle, then it is an/a:
obtuse triangle
right-angled triangle
acute triangle
equilateral triangle
A
1003076801
Level:
A
\( ABC \) is a triangle with sides \( a \), \( b \), \( c \). Let \( a\leq b\leq c \). Two of its interior angles have measures of \( 70^{\circ} \) and \( 50^{\circ} \). Which of the following statements about the triangle \( ABC \) is true?
The third interior angle is opposite the side \( b \).
The angle of the measure \( 70^{\circ} \) lies opposite the side \( a \).
The angle of the measure \( 50^{\circ} \) lies opposite the side \( b \).
The third interior angle is opposite the side \( c \).
1003021711
Level:
A
What is the measure of all interior angles in an equilateral triangle?
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 90^{\circ} \)
\( 45^{\circ} \)
1003021710
Level:
A
In a right-angled triangle \( ABC \) with a right angle at the vertex \( A \) the measure of the angle \( ABC \) is \( 50^{\circ} \). Give the measure of the angle \( BCA \).
\( 40^{\circ} \)
\( 90^{\circ} \)
\( 30^{\circ} \)
\( 180^{\circ} \)
1103021709
Level:
A
The picture shows an isosceles triangle \( ABC \) with the base \( AB \). Calculate the measure of the angle \( \alpha \).
\( 31^{\circ} \)
\( 62^{\circ} \)
\( 118^{\circ} \)
\( 59^{\circ} \)
1103021708
Level:
A
What is the measure of the angle \( \alpha \)? (See the picture.)
\( 7^{\circ} \)
\( 76^{\circ} \)
\( 83^{\circ} \)
\( 16^{\circ} \)
1003021707
Level:
A
Choose the false statement.
All altitudes in a right-angled triangle are perpendicular to one another.
The centroid of a triangle divides each median in the ratio \( 2:1 \).
The midline of a triangle is parallel to the third side and half as long.
The medians of a triangle intersect in a single point, the centroid of a triangle.
1103021706
Level:
A
In the triangle \( ABC \), \( \alpha=80^{\circ} \) and \( \beta=70^{\circ} \) (see the picture). Determine the measure of the angle between the altitude to the side \( AB \) and the altitude to the side \( BC \).
\( 70^{\circ} \)
\( 120^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)
1003021705
Level:
A
Calculate the measures of interior angles \( \alpha \), \( \beta \) and \( \gamma \) of a triangle if \( \gamma=2\beta \) and \( \beta=3\alpha \).
\( \alpha=18^{\circ};\ \beta=54^{\circ};\ \gamma=108^{\circ} \)
\( \alpha=15^{\circ};\ \beta=45^{\circ};\ \gamma=90^{\circ} \)
\( \alpha=12^{\circ};\ \beta=54^{\circ};\ \gamma=111^{\circ} \)
\( \alpha=54^{\circ};\ \beta=18^{\circ};\ \gamma=108^{\circ} \)
1103021704
Level:
A
Decide according to the diagram, which of the line segments \( a \), \( b \), \( c \), \( d \), \( e \) is the longest.
\( d \)
\( a \)
\( b \)
\( c \)