Construct Geometric Shapes With Conditions - 7th Grade Math
Card 1 of 25
What does $SAS$ tell you about the number of possible triangles from two sides and the included angle?
What does $SAS$ tell you about the number of possible triangles from two sides and the included angle?
Tap to reveal answer
$SAS$ determines exactly one unique triangle (if possible). Two sides and their included angle fix the triangle's shape.
$SAS$ determines exactly one unique triangle (if possible). Two sides and their included angle fix the triangle's shape.
← Didn't Know|Knew It →
What does $AAA$ determine about a triangle: unique triangle, similar triangles, or no triangle?
What does $AAA$ determine about a triangle: unique triangle, similar triangles, or no triangle?
Tap to reveal answer
$AAA$ determines similar triangles only (not a unique size). Three angles define shape but not size; all triangles are similar.
$AAA$ determines similar triangles only (not a unique size). Three angles define shape but not size; all triangles are similar.
← Didn't Know|Knew It →
What is the triangle angle-sum rule that must be true for any triangle?
What is the triangle angle-sum rule that must be true for any triangle?
Tap to reveal answer
The angles must satisfy $A+B+C=180^\circ$. The sum of interior angles in any triangle equals $180^\circ$.
The angles must satisfy $A+B+C=180^\circ$. The sum of interior angles in any triangle equals $180^\circ$.
← Didn't Know|Knew It →
What does $SSS$ tell you about the number of possible triangles from three side lengths?
What does $SSS$ tell you about the number of possible triangles from three side lengths?
Tap to reveal answer
$SSS$ determines exactly one unique triangle (if possible). Three sides uniquely define a triangle's shape and size.
$SSS$ determines exactly one unique triangle (if possible). Three sides uniquely define a triangle's shape and size.
← Didn't Know|Knew It →
What does $ASA$ tell you about the number of possible triangles from two angles and the included side?
What does $ASA$ tell you about the number of possible triangles from two angles and the included side?
Tap to reveal answer
$ASA$ determines exactly one unique triangle. Two angles and their included side uniquely define the triangle.
$ASA$ determines exactly one unique triangle. Two angles and their included side uniquely define the triangle.
← Didn't Know|Knew It →
What does $AAS$ tell you about the number of possible triangles from two angles and a non-included side?
What does $AAS$ tell you about the number of possible triangles from two angles and a non-included side?
Tap to reveal answer
$AAS$ determines exactly one unique triangle. Two angles determine the third; with one side, the triangle is unique.
$AAS$ determines exactly one unique triangle. Two angles determine the third; with one side, the triangle is unique.
← Didn't Know|Knew It →
Which of these can form a triangle: side lengths $6$, $7$, and $12$?
Which of these can form a triangle: side lengths $6$, $7$, and $12$?
Tap to reveal answer
Yes; $6+7>12$ and the other inequalities hold. All three inequalities satisfied: smallest two exceed largest.
Yes; $6+7>12$ and the other inequalities hold. All three inequalities satisfied: smallest two exceed largest.
← Didn't Know|Knew It →
Which of these can form a triangle: side lengths $3$, $4$, and $8$?
Which of these can form a triangle: side lengths $3$, $4$, and $8$?
Tap to reveal answer
No; $3+4\not>8$. Violates triangle inequality: $3+4=7<8$.
No; $3+4\not>8$. Violates triangle inequality: $3+4=7<8$.
← Didn't Know|Knew It →
What tool is used to copy a side length precisely when constructing triangles by hand?
What tool is used to copy a side length precisely when constructing triangles by hand?
Tap to reveal answer
A compass (or a ruler marked with the length). Compass arcs ensure exact length transfer in constructions.
A compass (or a ruler marked with the length). Compass arcs ensure exact length transfer in constructions.
← Didn't Know|Knew It →
What is the first construction step for a triangle given $SSS$: $a$, $b$, and $c$?
What is the first construction step for a triangle given $SSS$: $a$, $b$, and $c$?
Tap to reveal answer
Draw a base segment equal to one given side length. Start with any side as the foundation for construction.
Draw a base segment equal to one given side length. Start with any side as the foundation for construction.
← Didn't Know|Knew It →
Identify the condition that can produce $0$, $1$, or $2$ triangles: $SSS$, $SAS$, $ASA$, $AAS$, or $SSA$.
Identify the condition that can produce $0$, $1$, or $2$ triangles: $SSS$, $SAS$, $ASA$, $AAS$, or $SSA$.
Tap to reveal answer
$SSA$ (two sides and a non-included angle). Ambiguous case: the non-included angle creates uncertainty.
$SSA$ (two sides and a non-included angle). Ambiguous case: the non-included angle creates uncertainty.
← Didn't Know|Knew It →
Which inequality must be true for side lengths $a$, $b$, and $c$ to form a triangle?
Which inequality must be true for side lengths $a$, $b$, and $c$ to form a triangle?
Tap to reveal answer
$a+b>c$, $a+c>b$, and $b+c>a$. Triangle inequality: sum of any two sides exceeds the third.
$a+b>c$, $a+c>b$, and $b+c>a$. Triangle inequality: sum of any two sides exceeds the third.
← Didn't Know|Knew It →
If a triangle has sides $4$ and $9$, what is the possible range for the third side $x$?
If a triangle has sides $4$ and $9$, what is the possible range for the third side $x$?
Tap to reveal answer
$5<x<13$. Triangle inequality: $|9-4|<x<9+4$.
$5<x<13$. Triangle inequality: $|9-4|<x<9+4$.
← Didn't Know|Knew It →
What is the third angle if two angles are $35^\circ$ and $65^\circ$?
What is the third angle if two angles are $35^\circ$ and $65^\circ$?
Tap to reveal answer
$80^\circ$. Third angle = $180^\circ - 35^\circ - 65^\circ = 80^\circ$.
$80^\circ$. Third angle = $180^\circ - 35^\circ - 65^\circ = 80^\circ$.
← Didn't Know|Knew It →
Identify if angles $90^\circ$, $60^\circ$, and $40^\circ$ make a triangle: unique, more than one, or none.
Identify if angles $90^\circ$, $60^\circ$, and $40^\circ$ make a triangle: unique, more than one, or none.
Tap to reveal answer
None; $90+60+40=190^\circ\ne180^\circ$. Angle sum exceeds $180^\circ$, violating triangle rule.
None; $90+60+40=190^\circ\ne180^\circ$. Angle sum exceeds $180^\circ$, violating triangle rule.
← Didn't Know|Knew It →
Identify if angles $50^\circ$, $60^\circ$, and $70^\circ$ make a triangle: unique, more than one, or none.
Identify if angles $50^\circ$, $60^\circ$, and $70^\circ$ make a triangle: unique, more than one, or none.
Tap to reveal answer
More than one; $AAA$ gives similar triangles since $50+60+70=180$. Angles sum to $180^\circ$ but don't specify size.
More than one; $AAA$ gives similar triangles since $50+60+70=180$. Angles sum to $180^\circ$ but don't specify size.
← Didn't Know|Knew It →
Determine the result: do angles $60^\circ$, $60^\circ$, and $60^\circ$ form a triangle?
Determine the result: do angles $60^\circ$, $60^\circ$, and $60^\circ$ form a triangle?
Tap to reveal answer
Yes, one triangle (sum is $180^\circ$). Three $60°$ angles sum to exactly $180°$ (equilateral).
Yes, one triangle (sum is $180^\circ$). Three $60°$ angles sum to exactly $180°$ (equilateral).
← Didn't Know|Knew It →
Determine the result: do angles $90^\circ$, $45^\circ$, and $50^\circ$ form a triangle?
Determine the result: do angles $90^\circ$, $45^\circ$, and $50^\circ$ form a triangle?
Tap to reveal answer
No triangle (sum is $185^\circ$, not $180^\circ$). Angles sum to $185°$, exceeding the required $180°$.
No triangle (sum is $185^\circ$, not $180^\circ$). Angles sum to $185°$, exceeding the required $180°$.
← Didn't Know|Knew It →
Determine the result: can side lengths $3$, $4$, and $7$ form a triangle?
Determine the result: can side lengths $3$, $4$, and $7$ form a triangle?
Tap to reveal answer
No triangle (since $3+4=7$ is not $>7$). Triangle inequality fails: $3+4=7$ not greater than $7$.
No triangle (since $3+4=7$ is not $>7$). Triangle inequality fails: $3+4=7$ not greater than $7$.
← Didn't Know|Knew It →
Which option gives a unique triangle: $AAA$ with angles $30^\circ$, $60^\circ$, $90^\circ$ or $ASA$ with the same angles and a side?
Which option gives a unique triangle: $AAA$ with angles $30^\circ$, $60^\circ$, $90^\circ$ or $ASA$ with the same angles and a side?
Tap to reveal answer
$ASA$ gives a unique triangle; $AAA$ does not. Including a side length makes the triangle size definite.
$ASA$ gives a unique triangle; $AAA$ does not. Including a side length makes the triangle size definite.
← Didn't Know|Knew It →
What is the key step to construct a triangle from $SAS$ after drawing one given side?
What is the key step to construct a triangle from $SAS$ after drawing one given side?
Tap to reveal answer
Construct the included angle, then mark the second side length on that ray. The angle between sides positions the second side correctly.
Construct the included angle, then mark the second side length on that ray. The angle between sides positions the second side correctly.
← Didn't Know|Knew It →
What is the key step to construct a triangle from $ASA$ after drawing the given side?
What is the key step to construct a triangle from $ASA$ after drawing the given side?
Tap to reveal answer
Use a protractor to draw the two given angles at the endpoints. Angles at endpoints extend to meet at the third vertex.
Use a protractor to draw the two given angles at the endpoints. Angles at endpoints extend to meet at the third vertex.
← Didn't Know|Knew It →
Find the missing angle: $A=35^\circ$ and $B=65^\circ$. What is $C$ in a triangle?
Find the missing angle: $A=35^\circ$ and $B=65^\circ$. What is $C$ in a triangle?
Tap to reveal answer
$C=80^\circ$. Using $A+B+C=180°$: $35°+65°+C=180°$, so $C=80°$.
$C=80^\circ$. Using $A+B+C=180°$: $35°+65°+C=180°$, so $C=80°$.
← Didn't Know|Knew It →
Determine the result: can side lengths $5$, $6$, and $10$ form a triangle?
Determine the result: can side lengths $5$, $6$, and $10$ form a triangle?
Tap to reveal answer
Yes, one triangle (since $5+6>10$). All three inequalities satisfied: $5+6>10$, $5+10>6$, $6+10>5$.
Yes, one triangle (since $5+6>10$). All three inequalities satisfied: $5+6>10$, $5+10>6$, $6+10>5$.
← Didn't Know|Knew It →
What is the name of the ambiguous triangle case that can produce $0$, $1$, or $2$ triangles?
What is the name of the ambiguous triangle case that can produce $0$, $1$, or $2$ triangles?
Tap to reveal answer
$SSA$ (the ambiguous case). Two sides and a non-included angle can yield multiple solutions.
$SSA$ (the ambiguous case). Two sides and a non-included angle can yield multiple solutions.
← Didn't Know|Knew It →