Questions tagged [congruences-geometry]

For questions about congruent geometric figures, e.g., determining whether one figure is congruent to another.

129 questions
Filter by
Sorted by
Tagged with
1 vote
31 views

Simple request for help with geometric transformations and a problem I have.

The question I have a problem where I have been given four options, but as far as I can tell, none of them are correct. Can someone help me understand the process of proving similarity? So to my ...
• 11
37 views

reflexive property of congruence

While exploring basic geometry with my artist friend, she raised a question that neither of us could answer satisfactorily. Until today I thought that Hilbert's axiomatization of Euclidean geometry is ...
244 views

34 views

Show the congruence $YZ+JK=JF$ in this square with trapezoids, triangles constructed with square's midpoints

Show that $YZ+JK=JF$ I tried Pythagorean theorem. OG: Area of a square inside a square created by connecting point-opposite midpoint
248 views

Prove that $\angle AED = 2 \cdot \angle BEC$

Let $ABCDE$ be a pentagon such that $AE = ED$, $BC = DC + AB$ and $\angle BAE + \angle CDE = 180°$. Prove that $\angle AED = 2 \cdot \angle BEC$. So, by constructing it in Geogebra, I noticed that if ...
• 619
1 vote
45 views

Show the equality of two congruence transformations (geometry)

I have some problems in the following task of my geometry studies: Let $A,B,C$ three non-collinear points in $\mathbb{R}^2$ and let $T_1,T_2:\mathbb{R}^2\rightarrow\mathbb{R}^2$ two congruence ...
88 views

Definition of congruence of triangles.

In school level geometry,we studied congruence of triangles.Where it is defined that two triangles are congruent if they have same shape and size.But this is not a precise definition,what does it mean ...
• 3,703
29 views

polyhedrons congruent if faces are all congruent + same connection status?

In 2 dimension, a unit square and a unit rhombus(of certain angle) has the same list of edges and connection status. But the unit square and the unit rhombus are not generally congruent. Can we find ...
• 305
308 views

How to prove that angle bisector of right angle triangle ABC right angled at B is perpendicular bisector of third side AC. [closed]

I have tried using sine theoram, angle bisector theoram, congruency of type RHS,AA,ASA but haven't been able to do this.
1 vote
33 views

Congruent triangles that do not use reflections

This is a simple question on terminology in geometry: Suppose $ABC$ and $DEF$ are two triangles that are congruent, but the transformations from one to the other are based solely only on translation ...
• 4,925
252 views

Sources for IMO Geometry Theorems

The International Mathematical Olympiad contains highly non-standard problems involving the geometry of circles, triangles and lines which usually draws upon quite a few theorems and facts not ...
• 161
273 views

$PQ ∥ BC$ for isosceles $\triangle ABC$ and inscribed equilateral $\triangle PQR$ with $R$ being midpoint of $BC$

Triangle $ABC$ is isosceles. An equilateral triangle $PQR$ is inscribed in it with $R$ being the midpoint of $BC$. How can you prove $PQ \parallel BC$?
• 45
1 vote
156 views

How to proof the mid-point theorem without triangle congruence theorems?

Is there a way for me to proof the mid-point theorem without using the triangle congruence theorems? I can't seem to find one that's not using the triangle congruence theorems. The reason I'm trying ...
1 vote
1k views

Is triangle congruence considered as theorems or postulates?

Is triangle congruence like $SSS$, $SAS$, $ASA$ and $AAS$ considered as theorems or postulates? I've seen some people calling it as theorems and some other people calling it as postulates. What I know ...
27 views

Does there exist an efficient way to determine if two $n$-simplices in $\mathbb{R}^n$ are congruent?

Given two $n$-simplices in $\mathbb{R}^n$, does there exist an algorithm to determine if they are congruent which has a time complexity of the form $O(n^c)$ where $c$ is a constant? I'm assuming that ...
• 357
262 views

Prove ABC,A'B'C' are congruent:D is on BC,D' is on B'C', $\angle BAD \angle CAD= \angle B'A'D' \angle C'A'D', AB=A'B', AC=A'C', AD=A'D'$

In $\triangle ABC$ and $\triangle A'B'C'$, $D$ is a point on line segment $BC$ and $D'$ is a point on line segment $B'C'$. $\frac{\angle BAD}{\angle CAD}=\frac{\angle B'A'D'}{\angle C'A'D'}$, $AB=A'B'$...
1 vote
497 views

Triangle and Median related question

Let BD be a median in triangle ABC. The points E and F divide the median BD in three equal parts, such that BE = EF = FD. If AB = 1 and AF = AD, find the length of the line segment CE. I have tried ...
• 164
1 vote
250 views

Find the measure of $\angle G$ in a triangle

In the following figure, $\Delta$ADB, $\Delta$PCB and $\Delta$EFG are right triangles. $PB=AE$,$AC=CB$. Question: What is the value of $\angle G$? I figured out $\angle A = \angle CPB$ , $EF=AC$. ...
• 2,348
92 views

Geometry find the angle

Good day, excuse me, I am looking at congruence themes in Geometry, and I am trying to solve this problem, but I am not sure how to proceed. The coloured numbers is what I have so far (although now ...
1 vote
588 views

Similarity by SSA (side-side-angle) in obtuse triangles

Source: Challenge and Thrills of Pre-College Mathematics, Page 74, Problem 54: "In two obtuse triangles, an acute angle of the one is equal to an angle of the other, and sides about the other ...
• 187
248 views

Finding side lengths of a trapezoid given the distance between its diagonal intersection and midpoint of a diagonal

The Question My friend recently gave me a problem that I was interested in, but could not completely solve. I've already constructed a diagram that roughly represents the problem, and it's below. ...
414 views

Let $ABCD$ be a square. Points $A,B,G$ are collinear. $AC$ and $DG$ meet at $E$ , and $DG$ and $BC$ meet at $F$.

Let $ABCD$ be a square. Points $A,B,G$ are collinear. $AC$ and $DG$ meet at $E$ , and $DG$ and $BC$ meet at $F$. If $DE = 15$ cm, $EF = 9$ cm, find $FG$. What I Tried: Here is a picture :- I have ...
• 4,260
626 views

In the diagram, $AB$ $||$ $EF$ $||$ $DC$ . Given that $AC + BD = 250$ , $BC = 100$ and $EC + ED = 150$, find $CF$.

In the diagram, $AB$ $||$ $EF$ $||$ $DC$ . Given that $AC + BD = 250$, $BC = 100$ and $EC + ED = 150$, find $CF$. What I Tried: Here is the diagram :- I have assigned variables for the different ...
• 4,260
1 vote
372 views

$\Delta ABC$, $AC = 2BC$ and $\angle C = 90^\circ$ and $D$ is the foot of the altitude from $C$ onto $AB$. Find $AE : EC$ .

$\Delta ABC$, $AC = 2BC$ and $\angle C = 90^\circ$ and $D$ is the foot of the altitude from $C$ onto $AB$. A circle with diameter $AD$ intersects the segment $AC$ at $E$. Find $AE : EC$. What I Tried:...
• 4,260
442 views

In $\Delta ABC,$ side $AC$ and the perpendicular bisector of $BC$ meet at $D$, where $BD$ bisects $\angle ABC$.

In $\Delta ABC,$ side $AC$ and the perpendicular bisector of $BC$ meet at $D$, where $BD$ bisects $\angle ABC$. If $CD = 7$ and $[\Delta ABD] = a\sqrt{5}$ , find $a$ . What I Tried: Here is a picture:...
• 4,260
691 views

• 4,260
99 views

• 4,260
170 views

In $\Delta ABC$, $AC = BC$ and $\angle C = 120^\circ$. $M$ is on side $AC$ and $N$ is on side $BC$ .

In $\Delta ABC$, $AC = BC$ and $\angle C = 120^\circ$. $M$ is on side $AC$ and $N$ is on side $BC$ such that $\angle BAN = 50^\circ$ and $\angle ABM = 60^\circ$. Find $\angle NMB$ . What I Tried: ...
• 4,260
1 vote
In right $\Delta ABC$, $\angle C = 90^\circ$. $E$ is on $BC$ such that $AC = BE$. $D$ is on $AB$ such that $DE \perp BC$ .
In right $\Delta ABC$, $\angle C = 90^\circ$. $E$ is on $BC$ such that $AC = BE$. $D$ is on $AB$ such that $DE \perp BC$ . Given that $DE + BC = 1$ and $BD = \frac{1}{2}$, find $\angle B$. What I ...